Wow. You really need to reset everyone.
Toddler:
Needs her own room. Have her help set it up, but the bed in a corner, against a wall, with a bedrail. Let her go back to a crib if she wants to, but she needs to go to bed in her room and you need to hang tough for at least four days. Lights out, the same time, every night. Baby gate at the door so that she is not wandering around. If she gets so hysterical that she gets sick, clean her and it up, and back to bed. I promise, she won't starve and she will eventually learn to calm down because getting sick will not be a pleasant experience for her. Do not let her take the three hour nap - always two hours, max. Try giving her a snack before bed as she might be hungry in the middle of the night (nothing sugary). Invest in a kid clock that shows her when it is night time or day time, she can actually sleep with it and see it when she wakes up. Again, four nights will be really miserable. If you have to, sleep downstairs and let your husband not go in there but not let her hurt herself. You must get this straightened out because it will really go on until she is 8 or 9 - I have seen this whole thing with my brother's kids. It is a total nightmare. If you need no other inspiration, know that grandparents, siblings, etc., will not want to spend the night with your kids so that you can get away if they do not sleep.
Think about when it is time to move the baby out, too. I know that they are sweet and cuddly in the middle of the night, and closer, but they do actually sleep well on their own. Feeding every two hours leads to cuddling in bed, you not getting functional sleep because the baby is right there, your spouse not getting functional sleep because you are up fumbling around, etc. That is just shortening everyone's temper, with the upside probably being that the baby is sleeping during the day a lot, but probably starting to reverse days and nights (I have a 7yr old, 5 yr old, and an 8mth old, so I have been there, believe me). My pediatrician really likes to see the baby in his / her own room by four weeks. On our last one, we put her in there after a night. There are other factors in play, too, but she began sleeping 7 hours at a clip by 9 weeks (the first two did not, though).
I know that you are so tired that your toes probably hurt, but you are going to need to take the reins and bring some control to the situation. Your 2 yr old will respect you so much more if you lay down boundaries and actually stick to them. Consistency and known boundaries with kids are king. Studies show that both bring better self-esteem, better trust in the parent, and more affection from the parent. With the toddler, remember - she's 2, not 28 mths, she is not a baby anymore - they do not call them the terrible twos for nothing, and this is how she is visiting it on you. It is so hard to make that transition with the first one, but she really is becoming a kid.
Remember, you prepare the child for the path, not the path for the child.
Good luck!