Here's a set of intertwined questions and circumstances that many of us can relate to.  B is feeling stressed and confused about this situation. I'm going to take her email in parts. Please feel free to pitch in with your comments and support, as usual:

I'm not sure what to do, and my husband and I are kind of at an impasse
about this.  Our daughter just turned 1, and on occasion has nights where she is wide awake for 2
hrs – nothing seems to be wrong, but nothing seems to solve it. We
usually just rock her and eventually she falls back asleep.

To
help
hasten the sleep process, we've tried giving her pain meds (in
case of teething), a half bottle of milk, a sippy of water, cosleeping,
etc.
Nothing seems to work except time. We keep it quiet so she doesn't
think it's play time. But if we don't go into to get her, she cries
until picked up, so she isn't content to just play on her own in the
crib.

I've
always kind of chalked it up to
teething pains – she is a very slow teether and usually a few weeks
after these  episodes a tooth would appear.  We went through this with
the 9 month sleep regression too though. Right now she just has 2
bottom teeth, and those came in just in late May. I'd expect more are
on their way.

The
problem – lately she's been
female clingy lately, and quite the mama's girl.  Last night / this
morning she screamed – and I mean hysterical screaming at the top of
her lungs – for 45 mins when my husband came in to relieve me after an
hour.  (The hour she was with me, she just laid in my arms awake and
calm). I
went back into her room after the 45 mins of scream to take her back
from my husband, and he pitched
a fit.  He feels that I'm rewarding her with what she wants (me).  I
don't see it that way at all – I feel that it's our job to comfort her
and if she feels she needs me, damn it I am going to her.  I think it's
really unfair to let her scream for 45 mins to "teach her a lesson". It
would be different if it was 5 or 10 minutes, but it isn't. That has
happened on occasion too, but she surrenders much more quickly.  I
guess I draw the line at over 10 minutes.

So, first off, your baby is likely at a good age to start to make some changes in her sleeping habits if you're not keen on how they're going. In another part of her email, B. asked how separation anxiety affects sleep. We've talked about what could be going through a child's mind starting just before 1 years old and why those changes are likely to keep a child awake at night. But the peak of separation anxiety will likely have subsided by now. That doesn't mean the baby's not sensitive to separations  — now that she's passed through the "object permanence" gates of the 8-11 month period, your disappearances will always be somewhat fraught with meaning. But she should be settling down with the understanding that mommy doesn't disappear forever. So, if you want to apply your favourite, non-CIO sleep-training method (because you say you don't want to use CIO), I'd say go for it. It sounds like these long periods of wakefulness are tiring out your baby and certainly tiring for you and your husband.

Oh yes… I so feel for you. NO ONE is right or wrong in this situation. You both are just tired, frustrated, and you both desperately need a break. If you DO decide to use a systematic approach to sleep-training, I
think it's CRITICAL for you and your husband to get on board with a
plan TOGETHER. It is probably the only way you can maintain any consistency in your sleep-training approach.
If SOMETIMES you hold the baby for an hour and SOMETIMES your husband
goes in and attends to the baby and SOMETIMES he stays there and
SOMETIMES you can't take it and get the baby from him, it's going to be
very difficult for your baby to learn new sleep habits. So… my
suggestion would be for you to sit down one night after the baby IS
asleep and pour a glass of wine for the two of you (if you're into that
sort of thing… I find it a delightful way to begin a marital
discourse on any given parenting issue Then work out a plan
that BOTH of you feel good about following. If you don't think you can
allow your husband to do the soothing part of the sleep training, then
you make the commitment to always be the one doing it. This is a
perfectly reasonable strategy if your baby is going through a MOMMY
ONLY stage. Most babies do go through this. It's exhausting and often
infuriating and it can feel awfully rejecting to the parent who is
being… rejected. But I can assure you from a developmental perspective that your baby is not being manipulative (she doesn't have the cognitive capacity for that yet), nor will you spoil her to give her more mommy than daddy time; her behaviour is simply
evolutionarily adaptive. And VERY likely, she'll so get over you sooner or later and it'll be all about Daddy and how COOL he is and what a DRAG
you are. But until then, the mommy game may be the only game in town. That doesn't mean you can't sleep-train her; again, I won't tell you what method to use, but whatever you choose, it's likely to work a whole let better now than at 17/18 months. So, if you DO decide that you want to sleep-train and you want to be the one to take
on the major part of the soothing, that's fine; that's what feels right for you. But then I urge you to also give your husband responsibilities
during this sleep-training phase. Not only because you need some help, but also because he IS a valuable part of your family "team" and he needs to feel that his efforts are valued. Those efforts, at this stage, may not be best aimed at soothing the baby when she wakes because the baby has a clear goal of mommy. But he CAN do things to help. He can take the baby off your hands when she's less needy, for example, in the day or on the weekend and let you take a nap; he can rub your
feet while you go in and out of the baby's room at night, make you dinner, and
generally be a kick-ass cheerleader for you. You get the idea here… You guys are in this together and have the same goal: to raise a happy, healthy little girl.

Her screaming kills me emotionally. I feel so guilty when I give her to DH, like I instantly regret
it. I can't sleep when she is screaming like that, so I end up questioning why I didn't just
keep her so my husband can sleep, my daughter is calmer, and the neighbors don't think
we're murdering our child? 

It used to drive me BATTY to see my husband try to soothe the babies when he was unable to do it. I just wanted him to do it better or at least let me take over when he wasn't being effective. It is so hard for us mothers to remember that the father is, and should be, a large part of this child's world and even if our partners are not as good at soothing the baby as we are, they may need to give it a try, over and over, until they figure something out that works for them. 

I'll even go further… And please don't take what I'm about to say
as callous in any way. I have felt EXACTLY how you're feeling. But if
none of the sleep-training that you personally do works to minimize how
long your girl is awake at night, and you are really at your wit's end,
then try what I did the first time my boys were sleep-trained:
Let your husband take over the sleep-training, walk to your closest
restaurant, order a glass of wine (notice a theme here?) and a
main course. This latter part is crucial. Order a full meal so that
you are forced to stay away for an hour. (I remember that I actually had auditory hallucinations in the restaurant — I believed I could hear the cries all the way down the street). Repeat for three days. For
some, this may be disastrous. For others, like our family, after the
third day, I entered a quiet home, with children sleeping and a
husband who thought he was the most kick-ass Papa in town.

I think one of the crucial parts of B's email touches on the incredible stress
that a new baby puts on a marital relationship. There's a whole lot of
research on this "and baby makes three" phenomenon. Here's a review chapter
that you can actually read in its entirety, by one of the top scholars
in this field. This line of research has established that dealing with
the new challenges of infancy can put incredible, sometimes
irreparable, damage on a marital relationship. Did I need to tell most
of you this? Did you need tens of psychologists conducting 100s of
studies to prove this to you? My hunch: not so much. So many of us have
hissed at our partners to GET OUT NOW over our wailing baby's heads.
Countless mothers have felt the competing
desires to take a blessed break from our demanding child by handing him
off to our partner while at the same time wanting to grab the baby back
because YOU JUST AREN'T DOING IT RIGHT. So many of us have bit our tongues, sat on our hands, hid behind doors, willing ourselves to give our partner just 5 more min, just 2 more min, before we can't take the baby's cries for one second longer. It is so, so hard. For BOTH partners. But it DOES get easier, if the couple is willing to talk it out and even to have repeated conflicts that have the chance to repair. Withdrawing from one another, on the other hand, is often much more dangerous for the relationship in the long run. So if you can manage it — even in the middle of potentially the most stressful time in your marriage — keep the communication channels open. The whole family will be better for it.