you cant "make" him sign his rights over and the courts wont either, but you could at least take him to court and get full custody since he's putting forth no effort(which you would have to prove to a judge that he's just naturally avoiding you and the kids instead of working or something that pertains to that).. if you don't put him on the birth certificate for the second one you wont be able to get child support and he wont be able to see the baby unless he pays for a dna test in court(but this wouldn't affect your 3 year old, he would still have partial custody of her and be initialed to rights).. but the only way the courts would make the father sign over custody to the mother is if he was abusive to the kids or anything to do with that matter or if he leaves for more than 12 consecutive months without coming back(without giving you money to support her)
All I know is do not have him sign the birth certificate.It will make tthings easier if you don't want him around! Good luck