I recommend that you don't think about it this way.
Is mind-independent moral realism true? Geez. I don't know. (And, by the way, neither do you.) But here's some stuff I feel quite comfortable saying.
I want my kids to be empathetic. I want them to give a damn about how their actions affect other people. I want them to take seriously the idea that if they wouldn't be willing to put up with being treated in some way or other, then they'd better have a very good reason, and not just a selfish one, for treating other people that way. I want my kids to treat others decently. I want them to be honest. I want them to be fair. I want them not to be jerks.
Do I want all that because I'm convinced that mind independent moral realism is true? Nope. I want all that because I can't imagine not caring about such things. They seem right to me, and the fact that something called "mind independent moral realism" might not be true seems to me an awfully thin reason for turning my back on my considered judgment that I shouldn't be mean to people, let alone steal from them or cut the brake-lines on their cars.
I also want my kids not to be suckered into buying claims about what's "good" or "bad" that don't stand up to scrutiny. For example: if someone thinks that same-sex romantic relationships are "bad," this may end up making their lives miserable. But it's also moral baloney. The fact that some people think they're bad doesn't cancel the fact that the usual arguments meant to demonstrate this are lousy arguments—and not because they presuppose "mind-independent moral realism." Moral grown-ups who think some things are morally wrong and others are morally right don't think that just because they've been told these things. Moral grown-ups are perfectly capable of seeing through bad moral arguments.
But notice something else. You're looking for advice about how you should raise your kids. You want to know whether you should teach them the highly theoretical and disputable view that you call mind-independent realism or whether you should teach them the highly theoretical and disputable view you hold. You might protest that you're really just asking which approach is less likely to lead to harm for them. But don't you think (leave philosophy aside for the moment) that we should care about what might harm our children? That it would be a bad thing not to worry about this?
This isn't a "gotcha" question. I'm not saying that if you answer yes, you're committed to "mind independent moral realism." I don't know whether that would be true or not, and for that matter, I don't know how much difference it makes to whether moral judgments can be right or wrong. I'm just suggesting that your real worry here isn't about an abstract philosophical question. It's about how best to raise a child—a child who has some hope to growing up to be a wise adult. That's very different from wondering about which abstract, disputable philosophical view you should try to imbue your child with. In this case, I suspect you're likely to do better if you approach deciding what to do from within the midst of things, so to speak, rather than with a highly theoretical idea as your guiding principle.
I recommend that you don't
I recommend that you don't think about it this way.
Is mind-independent moral realism true? Geez. I don't know. (And, by the way, neither do you.) But here's some stuff I feel quite comfortable saying.
I want my kids to be empathetic. I want them to give a damn about how their actions affect other people. I want them to take seriously the idea that if they wouldn't be willing to put up with being treated in some way or other, then they'd better have a very good reason, and not just a selfish one, for treating other people that way. I want my kids to treat others decently. I want them to be honest. I want them to be fair. I want them not to be jerks.
Do I want all that because I'm convinced that mind independent moral realism is true? Nope. I want all that because I can't imagine not caring about such things. They seem right to me, and the fact that something called "mind independent moral realism" might not be true seems to me an awfully thin reason for turning my back on my considered judgment that I shouldn't be mean to people, let alone steal from them or cut the brake-lines on their cars.
I also want my kids not to be suckered into buying claims about what's "good" or "bad" that don't stand up to scrutiny. For example: if someone thinks that same-sex romantic relationships are "bad," this may end up making their lives miserable. But it's also moral baloney. The fact that some people think they're bad doesn't cancel the fact that the usual arguments meant to demonstrate this are lousy arguments—and not because they presuppose "mind-independent moral realism." Moral grown-ups who think some things are morally wrong and others are morally right don't think that just because they've been told these things. Moral grown-ups are perfectly capable of seeing through bad moral arguments.
But notice something else. You're looking for advice about how you should raise your kids. You want to know whether you should teach them the highly theoretical and disputable view that you call mind-independent realism or whether you should teach them the highly theoretical and disputable view you hold. You might protest that you're really just asking which approach is less likely to lead to harm for them. But don't you think (leave philosophy aside for the moment) that we should care about what might harm our children? That it would be a bad thing not to worry about this?
This isn't a "gotcha" question. I'm not saying that if you answer yes, you're committed to "mind independent moral realism." I don't know whether that would be true or not, and for that matter, I don't know how much difference it makes to whether moral judgments can be right or wrong. I'm just suggesting that your real worry here isn't about an abstract philosophical question. It's about how best to raise a child—a child who has some hope to growing up to be a wise adult. That's very different from wondering about which abstract, disputable philosophical view you should try to imbue your child with. In this case, I suspect you're likely to do better if you approach deciding what to do from within the midst of things, so to speak, rather than with a highly theoretical idea as your guiding principle.