AITA for refusing to keep providing my sister free childcare because of BIL’s choices?

TLDR: I found out the reason my sister couldn’t afford babysitters is because BIL has been sending half his income to his family so I stopped providing them free childcare, AITA?

My husband 44m and I 38f live in NYC with our 8yr old daughter and have a live in nanny because we’re both doctors with unpredictable crazy hours. My sister 33f "Anne" and her husband 32m "Sam" also live in NYC 30ish mins from us with their 2 kids 4&5. Sam is originally from India, and only came to the US for his masters before getting a job and marrying my sister.

Last dec my sister told me she and her husband were struggling to afford childcare (especially extended winter break hours) for her two kids, and asked if my nanny could also watch her kids too. I talked it over with my husband and we agreed. I asked my nanny if she was willing to and offered her a 27k/yr (~ 30%) raise to take care of 2 more kids. She agreed and for the past 7mo has been taking care of them 3-7pm m-f.

Weeks ago, I brought up to my sister if she could find temporary childcare for her kids, because my daughter is going to sleep away camp for a month and I wanted to give my nanny the time off. She begged me not to since daycares in NYC all have long waitlists and a babysitter 40hrs a week for a month would be 4k. I got concerned she couldn’t even pay for a month of babysitting for her own kids since I knew my sister’s salary is 70k/yr and BIL is a software engineer with a higher salary. I asked after her finances and she very reluctantly told me Sam had been giving almost half their income to his family in India, and was spending thousands to sponsor his siblings’ immigration process. I was furious at this and told them not only was I giving my nanny the vacation time, I was no longer willing to provide free child care.

This started a huge argument between Sam and I. I very harshly condemned him for putting his extended family above his own children. He didn’t take it very well and said his parents sacrificed to send him to school in the US and he is doing the right thing by paying them back.

My sister was happy I stood up for her (she privately admitted she hadn’t wanted to send that much money) at first but since then has been asking me to take her kids back because she and Sam are now constantly arguing over this. I told her I wasn’t going to enable Sam’s actions any longer, and that had I known I was paying 27k more so Sam could send money to his family, I never would’ve agreed to it in the first place.

My husband agrees with me, but has said maybe I should relent so my sister could have a happier marriage. Sam is calling me an asshole for his family suffer the loss of his money when it doesn't effect me much, Some of my friends who also know them thinks I’m wrong for making my sister and her kid’s life harder, esp since I will keep paying my nanny her new salary.

Edit: to be clear, my dilemma is because my sister loves her husband and doesn’t want to divorce him. So I could either try to talk her into leaving him, which would make her miserable, or just give them money to smooth this problem over, which I feel like would open me up to BiL asking me for more and more money one way or the other, because in his words “we’re family and we help each other when we have more”. Which is true that I could easily pay for his kids to have a more comfortable life than when they’re not with me.

Also, we pay a lot of taxes here in nyc, especially if you make 6 figures, plus their mortgage for a 2bd apartment is 4k/month and that’s not counting all the other costs of living. I didn’t mean to say BiL was sending 100K to his family, I mean he was sending something like 2k/month (half of their income minus all their expenses) to family and using money saved from paying a babysitter to pay for an immigration attorney etc. My sister knew he wanted to help his family come here and I think she knew in the “I want to be close to my family” sense and not the “I would prioritize helping them move here above our kids” sense and now she’s in too deep.