Divorce for expats in Dubai and custody of a child

My relationship with my wife has ended and I am seeking a divorce. Reconciliation is not an option and the divorce will not be amicable. We have an Islamic wedding contract and also an EU wedding contract. We are both expats (different nationalities) but I am a Muslim and she isn’t. We have an infant daughter.

My wife insists on our daughter living with her but giving me rights to visit and take her on weekends. She expects me to pay everything to keep up with her current lifestyle, e.g. rent, bills, nanny's salary, car, etc. If I don’t, she has threatened to leave the UAE with our child. My wife is working but claims not to earn enough.

I also have a strong suspicion with some proof that my wife is having an extramarital affair with one or if not more partners.

Kindly seeking advice if I should seek a divorce through Shariah court? I would like to have the custody of my child. I have no objection over any claims on our assets.

Thank you.