Sending you a big hug indeed!! I am the mama of a very sleep-challenged 14 mo old DD. I was a nanny for several years when I was younger and helped my parents "sleep train" their infants. Apparently, I had the easiest babies in the world, b/c they never had to CIO, they just simply accepted their cribs and went to sleep. Oh, and if we were out and they got tired - they just went to sleep on their own. So that's how I pictured life with my baby to be, bought my pretty crib, etc (certainly NEVER thought I would co-sleep past very early infancy!!!!). I did plan to b-f so I started out with a co-sleeper. After about the 3rd night I gave up trying to place DD in it as she would just start to stir, grunt, eventually cry within 10 minutes of being put down. Mine or DH's chest was the only place she'd settle. Same with naps - after about 6 weeks she couldn't go to sleep on her own, even on the boob (and forget sleeping in the car, no love for her there, either). So I started holding her for naps - and getting her to finally snooze off by bouncing on an exercise ball, then slowly starting to feel the same things you are describing - can't do anything else, no free time, etc. I tried several no-cry solutions dutifully at several different points to no avail (i have a persistent one!!). In the midst of all of that, I started experimenting with different carriers and have been using them for all of her naps since then (yes, I have literally worn her for every. single. nap. for 14 mos. I don't "admit" this to most people b/c they think I'm looney or setting myself up for toddler issues, etc, all that stuff).
For me, I had to come to the conclusion that I believe deeply in my DD's needs. I do not believe she just "prefers" to sleep near me, I believe at this stage she genuinely needs me - that is just how she is wired. So I have made her sleep a priority and had to rearrange a great deal of things to do so (my house is not dirty but it is not as organized as my former self would've kept it, I have not been out of my house past 8pm save for 2 or 3 times since DD has been born, it is challenging to arrange outings/errands, etc, so carefully around her sleep, DH and I have had to get creative in the sex dept, etc) - BUT I have found that most of these things are truly not a great sacrifice in the grand scheme of things, and that changing my attitude/philosophy has been the greatest help of all.
That is not to say this hasn't been hard - REALLY hard, tearfully, I'm-so-tired-I'm-going-to-pass-out hard - at moments, but you can do it. Find a way to get yourself some sleep as well (if you can't lay down with your baby when they nap or don't have family in the area to stay with them for an hour while you sleep, hire a college student 2 or 3 days a week to be in the next room with your baby while you get in some sleep time, set a solid sleep-in and/or naptime routine on the weekends when DH is home, etc).
Look into new ways to get baby to sleep so you have a little more mobility - a ring sling, a MT, an Ergo, etc. And it sounds like co-sleeping would really help. At least then you are not staggering down the hall - and baby doesn't need to necessarily wake herself all the way up and get that much more outraged. You can just put her in bed and get a mesh bedrail, or if you'd like to try more space, sidecar her crib to the bed and see how that works for you. FWIW, at nighttime I wear DD for the first 2 hours of her sleep, then when she's deeply asleep (as deeply asleep as she gets, lol), I can lay down in bed with her and usually get her settled there pretty quickly. (Addressing the concept of co-sleeping: I jsut had to take it one day at a time and go with it as long as it worked. I tune out the "she'll be in your bed 'til she's 12" crap from random people, as I know that eventually this time will pass and she will sleep alone. In the same way that I would not think to push or force her towards other developmental milestones, I will not on this one, either.)
Try some sort of new motion: a ball, a swing, etc, other methods to get DD back to sleep quicker should she wake all the way up in the middle of the night (I have taken this exercise ball *everywhere* with me - planes, car trips, friends' houses who lived too far away to get back in time for nap time, etc!) And I second the PP suggestion of a sound machine - we white-noise it every time she falls asleep (just easier than her startling awake at some random little noise).
The Baby Sleep Book by Dr. Sears was a great help to me. I also have to say, watching my DD grow and thrive reinforces my choices for me a little bit more everyday. Not bragging on my DD, but I'm just saying she is bright, happy and engaged - and even when I am at my most tired, I know she has gotten the rest she needs and is benefitting greatly (and my day is ultimately so much easier as there are no longer stresses/battles over sleeping time - and no more dealing with a crabby-due-to-overtiredness kid).
And SUPPORT - as in, moms who feel you and are going through the same thing. I met 2 of them at LLL and would not have made it through this last year without them (or this message board, for that matter). I also found that I needed to work really hard to tune out naysayers, and even avoid some playdates if anyone was going to be judge-y or critical. That's the last thing you need when you're tired and vulnerable!
I totally hear you on the other kids thing. I thought the same exact thing at 4am the other morning, in fact!

Every baby is different, and there is no guarantee that they will all be sleep-challenged. Heck, if you had one of those "easy" babies next, it would be a cake-walk after this experience!

I take comfort in the fact that the majority of the people I've chatted with who have babes like ours say that things usually improve drastically around the 2 yr (or end of the molar arrivals) mark. So you can space your babes 3 years apart - not so bad? And of course you could get through it if you really wanted them closer, just saying there is an end in sight, even though it may not feel like it.
My very last thought is that basically every single new parent I know says they are tired for the first year or two. We all just are! It's all relative to everyone's experience: if you have some easy, crib-sleeping baby, when they wake up due to the inevitable teething, growth spurt, etc, those parents will be sooo tired during those moments. If you have a co-sleeping baby who wakes to nurse 4-6 times a night, the mom may be able to fall back asleep quickly - but she's still waking up 4-6 times a night! And what if dad is a light sleeper? I hope this part is coming out right; I'm not meaning it to sound like 'suck it up', but just to illustrate that everyone feels tired. There is a spectrum, of course, and you are definitely on the far side of it...
Trust your mama instinct and go with what you feel your individual baby needs. This time *will* pass - and it will also ebb and flow. I had moments of, 'ohh, we've made it over the hump' only to be foiled by 6 teeth coming in at once, etc, but truly, as they get older, it gets better and better bit by bit.
Sorry this turned into a novel... I feel passionately on this subject, and truly wish you the best!
Good luck.
