For school - I would send my daughter. For a couple of reasons - she is at a small enough school (it is almost a family as pretty much everyone knows each other) - there are only 17 kids in her class. So they are in a very good position to spread the kids out.
Kids talk, eat lunch together, share communal bathrooms, etc. Even if they are spread out, they are still exchanging exhaled air. Think about 17 people in a room with one person smoking. All 17 are going to be breathing the second-hand smoke.
Would you want your kids in a classroom everyday if there was just one person smoking in it? If not, why would you expose them to COVID19 or any other pathogen that is not part of a normal healthy immune system-building pathogen diet?
In addition she is in high school so it is easier in the sense that they can understand they need to have spacing, they need to wash their hands and so forth more so than say elementary kids.
Social distancing isn't going to work if the frequency of contact is daily, as in a school situation. You have to figure that every student in a school is also interacting at home, and the parents are all mostly going to workplaces while the kids are in school. So each of those venues is a hub for viral exchange, and even if people are social-distancing, that high-frequency of venue-attendance is going to bring up the speed with which any virus can work its way through a population.
Also, for her it is her mental state. She really needs this for her mental well being. I have been giving her more freedom to meet up with friends - this does not mean she is in large goods but like last night she went to a local small beach and her and couple friends hung out - but with distance.
Young people are the people most drawn to social contact away from their families. It is the time when they are programmed to leave the nest and seek out prospective mates and new friends. So of course young people are going to be the most mentally affected by contact restrictions, but they are also the most prone to spreading viruses.
In this case, it is worse than in the past when you could just rest assured if your kid avoided sexually transmitted diseases and pregnancy. Now we have to worry about pathogen exposure that's airborne. This is a whole new dimension of vulnerability.
“My high school kid is really struggling to focus in online school, and I’m at work and not able to monitor him. It feels like the same result as if he had dropped out, and I’m worried about his ability to keep up.”
It is going to be a huge challenge to incentivize and/or discipline students to work and progress without interactive supervision.
“The kids need school and activities. My kids are 9 and 5. They have become anxious, lonely, and bored, all of which contribute to more emotional acting out and some noticeable depression (especially in the older child). It is worth the relatively small risk to send them out so that they can be more socially stable.”
The only way it's going to be a small risk is if the parents of the kids all work in the same place and so the kids' families basically all form on single super-household that is isolated from other households.
This could work if people create combination office/schools where adults can work remotely from the same venue where their kids go to school. That way, you establish a limited network of contact that doesn't extend out through multiple workplaces where other adults have other kids in other schools.
I think each person has to work with what is best for them. I don't think any of these are cut and dry and each situation is so different for everyone.
Pathogens go wherever they can, using whatever bodies will host them.