I think you are. You have recognized the importance of having him in her life, but you have also taken steps to protect her. He might think that "she won't remember", but there is an impact from abuse even on babies. It often shows up as delayed development and sometimes difficult with attaching to people. Any counsellor could tell you about it.
Even though you are breastfeeding you are giving him a good block of time the I suspect is the whole length of time between feedings. I think that is all he could really hope for until she is weaned.
Given his history and present living situation you are trying to protect her. You do need to make sure he is not drunk (or drinking). If you have any suspicions do not let him have the visit and offer make up time another time when he is sober. Make it clear that you are only refusing because he has been drinking, and make a record of the reason and circumstances.
I've never heard of "bad first-time mom syndrome". I doubt it is a real thing. I suspect he is only saying that to intimidate you. What you have posted sounds like you are a capable of making responsible decisions. Make sure you get your agreements in writing and reviewed by a lawyer (and a awyer for him too).
As for the apartment you are only responsible if your name is on the lease. If it is then contact a community legal clinic for advice. If he has a roomate why can't he pay the rent? was the roomate there when you lived there? Did the roomate move in after? all of that info would help to know.
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