It sounds like this is a mess.
Are the children going to be at risk of harm in the mother's care? Or is this really just now a dispute between who should look after the children for the time being?
It sounds like his ex has made allegations in order to try and discredit him, which is obviously not a very pleasant situation.
Hopefully the police will see this for what it is, and release him with no charge and no further action.
If that isn't the case, they may put in place bail conditions which could impact on his ability to care for the children, which is perhaps exactly what his ex has done this for.
As far as the family law side of things goes, unless there is a court order or bail condition in place to state otherwise, both parents have equal rights to care for their children. If they cannot resolve this amicably then the case will have to go through mediation (if appropriate) and then to the family court.
Is there anything specific I can clarify about this or assist further with at this stage?