While there are some judges, perhaps even some jurisdictions, that are outliers, the answer to your question is: generally yes, no question about it.
While the preference for and favoritism showed mothers is not as great as it was a generation or more ago, and while fathers are gaining parity with mothers in child custody cases, the courts still generally favor mothers over fathers for no reason other than their being mothers. Sexual discrimination is still alive and well in the family courts.
Utah Family Law, LC | divorceutah.com | 801-466-9277
https://www.quora.com/Do-family-courts-favour-mothers/answer/Eric-Johnson-311