How do I keep my marriage while sweeping everything under the rug?

Different scenario, but we moved mom in with us a few years ago. She is a stroke and cancer survivor so required a lot of care. I was similar to your wife in feeling the responsibility to take on her care due to guilt I personally felt from taking her away from my father (due to mistreatment). I felt her world had been turned upside down, that she deserved better so let her consume my life....at the expense of my marriage. (It was so easy to slip back into my childhood role of caretaker.) My husband and I had several conversations where I pushed back and made excuses. We finally went to a marriage counselor and having an outside neutral party explain to me what I was doing to myself as well as my marriage was key. I still struggle with immense guilt as we have now moved mom into assisted living, but I was not seeing anything from my husbands perspective until we went to a counselor. Please dont give up on her and your family. Push hard for outside help. It is very hard to be caught between the relationship with the parent and your spouse/children. Good luck.

Do you have any older Filipino friends that you could trust to talk to your wife and her father? I was lucky; we wound up having my Lebanese FIL with us for many years, as he and my MIL did not live together well and she was a very strongminded person. Fortunately, my husband dealt with him, so I didn't have a problem with him--your brother-in-law probably would be better for FIL if he could be convinced that he needs to deal with him.

Have you tried counseling for yourself first to be able to cope with this situation? Then counseling for the both of you. Counseling will give you skills.

I am so sorry your family is going through this and make no mistake you are all going through some very difficult stuff. First I just want to remind you that while the cultural differences are a big part of what's coming between you at the moment your wife's culture is a very big part of who she is and I have to believe in turn a big part of what drew you to her and who you fell in love with. It is in turn also a big part of who your children are and while each generation makes their mark (changes) on traditions the roots often last many generations and is that such a bad thing? I mean it sounds like you suffered some of the broken family scars growing up, perhaps the deep rooted family ties are exactly what drew you to your wife and her family, there is so often a dark side to every positive... Just as there are, no doubt, things about your background that drew her to you. I'm in no way suggesting you are in the wrong or have no right to feel the way you do, I'm simply suggesting that the other players here, your wife, FIL & your children, all are seeing things through their own glasses, pain and experience and it might be helpful if you could all find a way to at least try and understand each others view.
In that vein a counselor who can help facilitate you each explain or present it makes a lot of sense and given the heavy difference in your wife's cultural influences coming into play here if you are OK with it and can find someone who is from or has a particular understanding of that, all the better. I admire and have often been jealous of families with such strong cultural roots, yet I also can't imagine some of the treatment (usually women) family members put up with because it's all they know, what they trust. I'm sure the same can be said for members of those cultures looking at my family or cultural base. So just as the right counselor can help your wife explain her gut and you understand (not necessarily agree) her roots they should be able to help you explain your reaction, lack of grasp and needs. I think at least for now focusing on you and your wife educating and opening up to each other but it might help pave the way for your wife to be able to ease her father into a new "reality" or help you and he communicate needs better.
I wonder too if maybe there is more medically/cognitively involved in your FIL's situation and even your wife's response (knowing it or not). They have both suffered a great loss and people deal with loss differently but just because your wife has steeped into her mothers shoes in the car of her father doesn't mean he thinks of her as his wife's replacement. Your wife's care and what seems to you favoring your her father over everyone else may be just as tied up in her grief (and miss-placed guilt) over the loss of her mom too, it wouldn't surprise me if once unpacked her suitcase is heavy with emotional reasons, beyond her awareness, for what is happening now and what she needs most is your love and support (not loosing yourself) to help her navigate through. The same may be true of your FIL, I don't know if there are cultural factors but the loss of his right arm may have him depressed, repressed and looking for a replacement so his daughter doesn't have to take over. If you & wife as a team can get geriatric professionals involved to help and use his desire to move on (with a new wife, if it happens or not) to steer him to decide he wants to move out now that he doesn't need help anymore and is able (wants) to be independent that is a far better scenario from you forcing him or expecting your wife to, better for kids too seeing you help each other through tough times rather than force your way through.
My heart really does go out to each of you and I hope that collectively you will find a way to work through it as a family and maybe understand each other more in the process making that family bond stronger, what a perfect legacy to evolve from your MIL's passing.

A separation might get her attention. I don’t advocate for divorce unless it is abuse or unfaithfulness but you need to save yourself and the kids!

JStatus: Enabling is going down a black hole that one cannot easily get out from. Picture this --- your wife has always enabled her dad and then if she pulls back, he may say "You (helped) me before; why now can't you assist me?" But something MUST change in this family dynamic, else it only worsens. Also, I see that he was codependent before his wife passed; your wife priorities need amendment. And I, too, would never burden my daughter with my care. Good luck and God bless you!
Llamalover47

OK so why isn't he moving out and into a place with his new wife? Seriously, please go to marriage counselling. This person will help you and spouse sort out all of what is going on here and there is a lot going on. There is so much going on that I hesitate to address it in this forum. This needs professional help. See if your health insurance will pay. If you go by yourself, that is more likely to happen. I believe that the marriage relationship should be of first priority and then your responsibility to your minor children and them anything else.

I wonder if there is a Filipino/Filipina counselor available in your area. Your wife may be more receptive to a counselor who shares her culture or, at the very least, is more similar to it than not. Asian cultures share similarities. I'd also look into some self-help books written by someone who knows the culture or comes from an Asian culture that is similar to the one your wife comes from. There is more than one belief system within every culture.