First of all, I really doubt you will be able to totally resolve this by March. It's totally up to you what you do. You can move over and make room for both babies in your room. Or you can refuse to go into her room until she cries herself back to sleep.
This is a very normal age for them to become very clingy. Sometimes they will cling on mom. Other times they will cling on dad. Even when they do love the provider, it's normal for them to feel serious separation anxiety at various points a long the way.
The fact that you have a baby coming will not make this any easier. Your child can sense that she is about to have to share you. You have talked about the baby and been excited as well you should.
There are those that believe a husband and wifes room should be a sanctuary and no children should ever be allowed. Then there are those people that realize that these kids grow up too fast and you'll have a lot of years in the future to get your privacy back.
Whatever you decide, take some big deep breaths. There are things about having kids 2 years apart that are fantastic and in some ways it's hard. But they will be so close in a few years. It's a great spacing. Just remember that this is supposed to be an exciting time, not a frustrating one.
As for cooking, put her in a highchair and give her some fat crayons, home-made edible playdough, toys etc when you are cooking and cleaning.
Suzi