Is it possible for a UAE court to oppose a judgment issued by a foreign country?

My ex-wife and I are of the same nationality, non-Muslims. We were married at home country and were divorced back home in Feb 2021.

The court back home granted custody to me. The children are 16 and 9 - all living with me in the UAE. They all go to school here in the UAE. However, she refused to go back home and now is an illegal alien living here in the UAE with an expired tourist visa with overstay fines of more than 6000 dhs.

She just hired a lawyer here in the UAE to try to take back the custody. Can she do that? Or to be precise, can the UAE court meddle with the court decree of the home country?