“If all of Shmerel’s classmates are going to theme parks, he may not be too happy about going to the neighborhood playground” -and he’d probably be really unhappy about going to the nursing home (if it’s the only Chol Hamoed trip). I would probably take the kids to something fun on Chol Hamoed and do the nursing home on Shabbos or Yomtov or in addition to the fun trip, but not instead of.
But I’m not sure I agree that Shmerel would be unhappy about going to the neighborhood park – that would depend on numerous factors such as how you have been raising your kids until now, does he have other friends going to the park, how old he is and how fun you are able to make it. A lot of the fun comes from the presentation. I also wouldn’t advise going to the NEIGHBORHOOD playground – that would not be an outing. The point is to get in the car and TRAVEL to a park you don’t usually go to.