As a matter of policy, at our house we have made the extra stuff optional. Don't like Math Circle because you'd rather be home reading comic books? That's okay; it was optional enrichment. Don't want to do your assigned homework? That's not even remotely okay and we will sit you down and make you do it well before you do the fun stuff.
We want our kids to have opportunities, and our house is loaded with interesting things to read and do, and so on. We also limit time spent on "junk activity" like video games. But I don't want them to feel like they have to do academic work above and beyond what school requires to please us as parents. They have enough "gotta-dos."
For my kids, feeling forced would absolutely make them do less of it, not more; feeling like it's optional makes it stay interesting and motivating for them. (And I will indeed sometimes let them off the hook for small household chores if they are busy with something worthwhile, which gives them an extra fillip of joy in doing optional but quality stuff.)
Every family has to do it differently, but that's what we do.
DeeDee
