Seeking guidance, expertise, advice or opinions given what I'm guessing is a fairly uncommon situation.

I'm an unhappy spouse who has been together with my wife since 2015 and married since 2017. We have a 4 year old and a newborn. I'm American and my wife is from Kenya. We were married in the Middle East (I was working there) in a non-religious, civil ceremony, but are now currently living in the EU as long term residents with plans to potentially naturalize (dual citizenship for me).

Our children were both born overseas but are American citizens. They do not have Kenyan citizenship. We never applied for a spousal green card for my wife and I have always filed taxes as married, filing seperately. I also haven't filed my marriage in any US state basically because I've lived outside the country for the last 11 years or so with just the odd visit to the states when my mother passed. I have funds from a home sale in a US Bank in my name. I bought the home long before I met my wife but sold it when we were together. House was solely in my name and I paid the capital gains tax myself.

We have a joint account in the EU and some savings accounts in our individual names as well as the kids. We also bought a house in the EU outright with the title in both our names.

Ok, so my question is what divorce laws would apply to our situation? She isn't a US green card holder and the only paper showing we are married comes from a middle eastern country. We are not EU citizens but do consider it our home/primary residence. One child was born in the middle east and the other in the EU. Neither country recognizes citizenship through birth rights.

If I was to divorce her, what financial responsibilities would I have legally? Whose laws would I have to follow? My priorities are custody of my kids, then savings/money, then the house in the EU. I could live having sole custody of my older daughter and giving my wife custody of the newborn given the situation. I am not looking to give her the majority of my money as that is earmarked for the kid's future. I am also not looking to pay alimony as she is horrible with money.

Anyone had a similar situation as an expat marrying a foreign national? My current situation seems untenable so I'm really looking to get my ducks in a row.