I think there are two sides to this here, as I’ll illustrate below.
On the one hand, a parent can encourage a child to consider something that the parent enjoyed. For example, I suggested to DH and his ex that we enroll DSD in a girls’ program that I had enjoyed as a child. She’s been a member for 3 years now and loves it. However, if she decided that she wanted to drop out, that would be her decision. I’d also like to teach her to play the piano, simply because I play (so we can save on lessons) and because I think it’s important that she have some instruction in music. Again, though, if she decided this isn’t something she wants to pursue as an adult, that would be okay. I don’t see this “living vicariously” as being a problem - you’re merely “encouraging” your child to try something that you enjoyed.
The flip side of this is telling a child that he/she HAS to do something because the parent wanted to or because it was what the parent did in the past. I’m a nurse, for example, It would be awesome if DSD decided that she wanted to be a nurse, too, or to do some work in the medical and allied health community. (Allied health is everything related to health care that isn’t medicine or nursing directly - for example, physical and occupational therapy, social work, dietetics, etc.) But I’m not going to force her into doing that. She said to me once, “Mom, do you and Daddy have a particular career you want me to choose?” I said, “No. The only career we want you to choose is the one that God calls you to do. The only thing we want you to do is to listen to and follow the Will of God for your life.” I suspect that she may end up in some kind of “helping” profession (she’s talking right now about teaching, for example) but that’s only because I think it would be well-suited to her personality. However, if she decided that she wanted to do, say, heavy mechanics or industrial engineering, I wouldn’t tell her that she can’t.