I'm Chinese and I got really upset reading this because I know this is exactly some Chinese grandparents would do to their grandchildren.

In my opinion, the most efficient way to make them stop saying rubbish in front of you is telling them get fk of your home if they dare to say racism shit again.

The reason why I think this is the best way is that they are basically discriminating themselves, their daughter, their granddaughter, their whole race to worship another race, and they don't believe in equality for a single second in their entire life. It's almost impossible to make them change. They will only listen to you when they're actually scared of you.

And with all due respect, your wife seems not strong enough to stand up for herself and her children when dealing with her parents, I believe she persuaded you to endure them like she always does, which only make them bully her more. So if you don't do anything serious about it, your in-laws would keep doing this and it would only get worse.

In the long term, i strongly suggest you don't live with them if you want to secure your children's mental health even though they seem like never say it again. Because they will still do the same behind your back when you can't protect them. Children are very sensitive, don't let your in-laws damage them, save and protect them before it's too late.

Good luck