Opinions Please

Ok so I'm 37 weeks. When I was 28 ish weeks my husband randomly came home one day and asked for a divorce. So I left and went to stay with my family in our home state. Fast forward to a week or two ago he asked if he could sign over his parental rights basically saying he wants nothing to do with me or our daughter. So I just stopped responding to the nonsense and I decided not to tell him when I go to the hospital or anything since clearly he wants no involvement. Early in my pregnancy he tried to pressure me into an abortion and threatened me with a divorce then, but he actually filed this time. 
My question is am I wrong for not telling anyone other than my mom and sister when I go to the hospital? I just don't want my daughter in an unstable environment & I feel like the wishy washyness will send me into post partum depression😭