Hoping to get custody

My stepdaughter has broken up with the father of her daughter. He keeps threatening to file for custody, so as a result of his threats my stepdaughter has decided to file. My granddaughter is in full time daycare and her parents split the costs for that. My concerns are that with the job my stepdaughter has it is appearing that she is only receiving part time hours and she seems to be ok with this and doesn't want to make an effort to look for a job that will give her 40 hours a week.

Is there a chance that when the custody hearing is held that a judge will say that because she is only willing to work part time to support her child, but she is fully capable to work full time and since her daughter does have day care that she would not be awarded custody? Then would the father get custody?

I've been trying to impress upon her that she needs to get a full time job, but she doesn't see why. She feels she at least does have a job.

It's more likely that the parents will get split or shared custody. The fact that she doesn't have a full time job probably would not affect that decision; however, when child support is calculated, it's possible that she will be imputed an income based on having a full time job. Depends on the state you live in.

Your stepdaughter will likely get custody (she is after all the woman), unless she is a crack whore turning tricks in front of the kid and her Ex is a church deacon. Even then, the cards are still stacked in the favor of the mother.
The father of her child doesn't stand a chance in hell of getting custody in the gender biased family court system, so your step daughter shouldn't worry about his threats.
I am not a lawyer.