if no paperwork has been filed with the courts then they have equal rights to the children. custody has not been established.
she needs to get a motion filed to determine the custody of the children. it is going to be nerve racking, but she has to hang in there. him denying her access to the child will only hurt him in the long run. but she needs to get the ball rolling.
an after thought for later. she might talk to the daycare provider - if she knows them well - and ask that anytime the father shows up for her to be notified before the child is released. i had a friend who had something simliar set up with her daycare provider. they had joint custody and the provider couldn't refuse the father. but the child was sleeping, or playing outside and needed cleaned up. things like that. and she would call the mother. she got away with stalling for a good five minutes or so. if she is close to the daycare, maybe it would be enough time.