Unlike many posters, I am not horrified by your financial set-up with your PIL. My DH is from the same background and although we don't do things in quite the same way as you do, I'm sure a lot of people would be shocked at some of the expectations on us to send money back home etc. I can see pros and cons to each approach tbh.
My own parents are not quite as far along the other end of the spectrum as yours... they wouldn't have ever charged me rent, for example, and we don't fuss too much over who is going to pay for a meal out or tickets to stuff etc. They wouldn't usually split the bill etc. So it was easy enough for me to understand how dh's family worked.
DH and I actually have separate money within our own household, although he does have access to a joint account with "my" money if he needs it. It's easier for us to manage it this way because then I can spend what I want to spend of "my" money and he can give as much as he likes of "his" money to his family without either of us having to feel too guilty. I cover all household costs (am the higher earner anyway) and don't really ask him to contribute. I know that lots of people would think this is a dreadful arrangement from my POV, but he grew up in poverty, his family is much less comfortable than we are, he was clear from when we first met that he would always need to support them, and I actually respect him for caring as much as he does. He did contribute quite a lot towards our house deposit, though I paid off the mortgage, and he gave me some money when I needed to buy a new car etc. We don't keep a tally between us, and we don't keep a record of what we have spent on his family either, which has substantial over the years. Occasionally, I will chip in towards family costs as well if needed. It actually works for us so no complaints. His family don't really know the details of what we earn, so I imagine that they just assume that all family money is shared. Fundamentally, despite our "separate money" set up, I think DH and I pretty much adopt that attitude too. If anyone in the family really needed money...on my side or his...it would be a no brainer that we would give it to them. That said, I think his family would share whatever they had with us if needed, and actually, my parents would always help out if needed too.
DH absolutely does not expect our dd (who is still at school but earning pretty good money from her PT employment!) to share her money with the household. He might be a bit
if she quibbled over a few quid...e.g. if she nipped out to buy milk and then demanded reimbursement, but actually, I don't think she ever would - she would be more likely to resist if we tried to give it to her. Her savings are very much her own and DH would always respect that. That said, I think dd has absorbed a lot of the "family" approach to money and I am almost certain that she will end up continuing to support the extended family in India out of choice when she is older.
It sounds to me that you have willingly made a lot of compromises over the years to go along with your DH's approach to family money, and it seems to be working for you well enough so I reckon that's all good. However, I think there should be at least some compromise on your DH's part with regard to the children... at the very least, if your parents give gifts of cash to the children, I think he should respect that. (After all, respect for elders is important in his culture
.)