Don't use him for childcare - ever
I did that thinking I was encouraging him to have a relationship with his child and he used to take my son straight round to any nutcase girlfriend of his who was around, dump him with her and go about his business.
I used to get calls from random women demanding i come and pick up my child.
So I stopped that and he took to demanding 'his rights' to see his son and would walk in and take him whenever he pleased day or night.
Then there was the time he didn't bring him back for 3 days and did not answer his phone, I was out of my mind with worry. I never got an explanation of where he was, my son came back with new clothes on and new toys and no sign of his old clothes or toys.
Then there was the time he decided to do some illegal minicabbing with my son in the back with the passengers
Then there was the time he decided to that to teach my son how to swim he would jump in a pool with him and hold him under the water so he would get used to it, almost drowned him the life guard had to intervene.
I could go on
Unstable nutters do not make good babysitters.
Don't let him get used to the idea that he has free access to your daughter, make sure he spends time with her with both of you present in a neutral place, not at your house - the park or a play area in a museum is good.
I agree, ask Uni about creche.