Few problems of mine:
- I can't get rid of my steward at on one of my homes, I'll ask her to be my follower, say we can part ways, and she goes right back to being a steward. This is the Dark Elf from the college btw.
- Whenever I try to purchase items(horse,carriage,etc) I'm pretty sure it registers to the other house. I bought a carriage and it ended up at the wrong house. When I try to buy a horse, it says I don't have a stable, when I do. Which makes me think its following my other home with nothing but a main hall.
- I have a bedroom quarters with a childs bed, chest, and drawers, but still says I can't adopt a child

You sound very confused McLovin.

Stewardship is a life time position in Skyrim, it is for one house only, you offered them the position so thay could look after the house. Any house improvements you ask from that steward, goes to their house, no matter where you have taken them. You can order wood from one steward and it is available at all three house sites, that is the only thing that is shared.

Considering your confusion about stewards, furnishing a house is a lot more complex. If in fact you have the right furniture to adopt a child, maybe you should finish furnishing the rest of the house? There are plenty of threads speaking about what furniture you need. If it will not let you adopt, go back and check you have everything you need in that room. For the bedroom wing you need 2 child's beds and 2 children's chests. For the main hall you need 2 single beds and the chest of drawers in between, as far as I know. I always got all the furniture so never had a problem.

Ahh thank you very much. I will try that. Is there a way to get my Steward back to the right house? And also, I can't ask anyone else to be my steward. Is it because she's there?

Having her there should make no difference to getting a steward for that house, but not everyone can be a steward, if you are in a hurry and do not feel like trying every follower you have we have an excellent thread on the topic of who will and will not be your steward.
http://www.gamesas.com/topic/1409356-unofficial-list-of-stewards/

The list is probably not complete yet, so you could always find someone new if you want to persist. For your current steward I would take her back to her own house and dismiss her there, that way she cannot get lost.