Maybe “I want my kids to have a solid foundation”

If they are still relatively young, it would sound more natural to say, "I want my children to have a steady upbringing". "Stand on solid ground" does not sound very natural/native to me. It sound to me like an idiomatic expression that one might find in a collection of idiomatic expressions, but in fact is not used "on the street", in casual conversation with friends and family, in the workplace, etc.

There is an idiom "stand on solid ground."

Like someone else already said, “I want my kids to have a solid foundation” seems to be the expression you’re looking for. “Foundation” is a term typically used to imply providing a support framework on which to build on, whether that’s literally in the case of buildings, or more metaphorically like in the case of providing your children a platform to build a good life for themselves.

Hey Sophia! Let’s talk :)