Hey. First calm down. 1) make sure you document every visit he makes and every visit he doesn't make 2) he has two DUI's, be assured that the court will definitely take that into consideration. 3) where's he living? Would she have her own bedroom? 4) make a list of everything you want to cover, what you want and valid reasons why.
Piece of advice: When you go back to court (and, you will) for custody, make sure that you request 1. no drinking or smoking near your daughter and no one can 2. no one under 18yr can babysit 3. Make sure you ask for first right of refusal 4. he needs your signed consent to take her out of state or county, if you prefer. 5. he needs to be responsible for pick up and drop off for his visits 6. ask for supervised visits (if they even grant him visits) because of his history of alcoholism.
I truly believe you are going to be okay. Do not panic. You cannot waste your time worrying about things you have no control over. Just make sure you start documenting EVERYTHING if you aren't already. And, when a question pops up regarding custody...write it down.
M 5yrs 1st baby-girl born 6/18/08 Bomb: 10/13/07 OW - I was 6wks Prego H Moved in w/OW: 11/2/07 D Final 07/10 OW had his baby 3/17/09-so her Me, now - happier than I ever was with him