Oh momma, I feel your pain.
I may get crap for it, but I don't think you can be as attached to twins as you can with a singleton. It's just too much. It takes so much out of you.
My boys are almost 4 months and I have been trying to make them a little less dependant on me than their sister was, because with her it was exhausting and she was just one baby.
Ok, on the bottle thing. It is going to be extremely difficult for you to get them to take a bottle from you. They know that you are right there with the goods, why would they take a bottle? You will have to enlist your dh or someone else to give it a try. You can try all different kinds of bottles, their are ones that are shaped like a breast that my friend had success with. Or at their age you can try a sippy cup. Have you introduced solids at all? That is something a sitter could give them if you wanted to be away for a couple hours. It would fill them up so they weren't hungry.
Sleeping thing. Oh sister, I hear you on this problem. I have read just about every sleep book so far in order to prevent any major problems. My dd was a horrible sleeper. I suggest reading some of the books I have read and then developing a plan and course of action and getting dh involved. Yes, I know he's tired and needs to work, but you need to be able to function. They are his kids too. The No-Cry Sleep Solution, Lull-a-baby Sleep Plan, Healthy Sleep Habits-Happy Child, Dr. Sears- The Baby Sleep Book. I would recommend reading all of them if you can, but the No-Cry, Healthy Sleep Habits and Dr. Sears are the top choices. They all have a little bit different approach.
But if what you are doing is not working for you, then change it. I know that exhausted feeling, it sucks. I hate not having patience and feeling so run down. Find some help. Pay for help. Your church, your friends- even if they have kids- could manage an hour, right?
Hang in there momma! Sorry everyone is sick, that doesn't help at all!