I do see why you want to sign over the deeds, if you are going to lose a grand then sod it, it's not worth the hassle, but on the other hand it could be enough to give you and DP the start you need, so it's got to be worth a free 30min consultation with a solicitor to find out.
I assume as your mother has been like this for the majority of your adult life, and possibly you childhood, you think this is 'normal' well it's not.
I think the main point you are missing is that she needs you more than you need her, I know she is your mother, but she is not your keeper.
The next time she treats you like a piece of shit on her shoe, stick up for yourself and let her know that you are fed up with it and won't be treated like that in front of your child, then leave, and let her stew for a while, absence makes the heart grow fonder!
You are not a doormat, I would not normally condone using a child in a battle of wills but I think you are an exception to the rule, you have what she loves, her grandchild, and if she can't be civil to you in front of your child then she needs to be taught a tough lesson so go kick some arse.