ADVICE NEEDED

My oh has a daughter to a girl he had a one night stand with and said he was unsure if he was the father but he wanted a DNA test to prove he was. She met a new boyfriend, didn't contact him again so he assumed the baby was not his (there was 3 potential fathers) when the baby was 7 months and she'd split with her boyfriend she got in contact done the DNA test let him see her once then stopped for another 4 months until they broke up again. We have his daughter 2-3 nights a week and one night every second weekend which is a Saturday night. Now she has met a new man and my OH wanted to change his Saturday to a Friday night which was fine until she said she'd collect her at 12pm which meant her only had her 2 hours before bed and she was away within 3 hours of being awake. Her excuse is her partner and her want to have his son and their daughter together for a weekend and he can have her the Sunday if he wants (she knows he can't with work) they've only been together 3 months and within the first month he had met their daughter and now meeting his son. My OH thinks it's far too son considering she wouldn't let him go to the hospital when their daughter was ill in case he took me with him and I was not allowed to meet her for near a year which I think is fair and when we moved in together she tried to get him to have her over his mums every Saturday night and come over hers alone during the week. He's not on the birth certificate and she won't put him on it what so ever, we don't even know if her ex is on it ! For some strange reason she's afraid to be taken to court to get a DNA test done and would not show him the results until after a year of the test being done. What options does he have? He's afraid if he takes her to court he'll lose days or she'll stop all contact during the case.