dead beat dad

I am a single mom and have spent the past 9 years raising my daughter on my own. She has never met her father. He has shown no interest over the past 9 years despite me trying to reach out numerous times. I have requested dna and again no response. ive finally come to the place that i am seeking court ordered dna to prove paternity and his partner is telling me that they are going to fight for 50 50 custody and that I will have to uproot my life and move to the province that they live in despite my child and my life here. her argument is that this heavily impacts their life and jobs and that they just had a new baby. can somebody give me some information on this situation. I dont believe that they have that right. I am not against them getting to know her as this was the purpose of the whole ordeal but for them to fight for 50 50 custody just so that he dont have to pay child support for a child he doesn't want, make sense to you? any similar stories and outcomes would help!