Execution petition- when to file

Dear All,

Family court has given custody to father and ordered mother to hand over custody in three weeks.  I am getting differing opinion on when I can file execution petition.

Some are saying that I shall do it right away, others are saying only after completion of three weeks as execution petition is in nature of contempt. Can you please advise what is right time?

Also if O.P  moves to high court and the court does not grant stay - will the family court proceed on execution petition?