Four hours in advance is standard policy for most airlines in the US. But the ticketed passengers have to be there anyway, so you can’t check anyone’s bags but yours. But, it may be cheaper to check two bags under your name rather than one under each name. My bags are always free so lots of times I check my kids’ stuff under my name.
We went to WDW right after picking up my two youngest after they were done with their respective years in college and between my husband and I, there were 4 free checked bags an not a single one was ours!
Same thing for getting printed boarding passes- the person must be there (unless you use a kiosk, I guess). Boarding passes are handier to have on your phone anyway. You can get them this way if you check-in online. My adult kids have their passes emailed to them, but I have the airlines’ apps so I use that.
You can have both your child’s pass and yours on your phone. And they can have their own on their phone, too, or you can have one printed out for them to carry. It’s is a good way to teach them responsibility without worrying about them losing it.
Personally, I’d get the kiddo from school early. It’s not worth the stress for an hour of school time at the end of the day. You could try to check all the bags under your name at 2pm, but I wouldn’t be surprised if they asked where the rest of your party was.