Our family has 3 switches. (2 are functional).
I'm having problems getting the same free downloadable content on both functioning switches, under different profiles.
The game in question is rocket League.
Son A is able to download and play rocket League under his profile on the first switch.
Son B is not able to download and play rocket League under his profile on the second switch.
When I attempt to download it it says I have already purchased. I don't know how to start it on the second profile. This would make sense if it was a paid game, I would just have to pay for the game again. But this is a free game so I'm not sure what the work around is.

Is the download being done from your eShop account? If so, you can only download it to one console. Each kid would need a separate eShop account to download to their own console. Nintendo is extremely strict with their online content.

I was looking into this type of sharing last year when we were looking at getting a second Switch console in the house. I didn't want to mess with having to set up and manage multiple eShop accounts, so we scrapped that plan. Their lack of family sharing seems to run counter to their advertising that wants you to buy a Switch for everyone in the house…

Yeah, that's the problem. Just seems weird for a free game...

That's not weird at all. It is not about the free game but the account in general.

It is absolutely weird. I have 2 xbox's and have no issue downloading the same game on both under my account. Nintendo is very consumer unfriendly despite their efforts to appear otherwise and are still stuck in the late 90s in terms of anything done online.

Nintendo has a 'home switch' system where any account can play any game that anyone has purchased on the home system but on other, satellite, systems an account can only play games that account has paid for (or cartridge games).

What you can do is make sure to set Son B's switch as the home switch then purchase all DLC through Son A. Then use Son A's account to download the game to each switch. Son A can play on their switch since even though it is not the home switch since their account paid for the game and son B can play it also with his own account because he plays on the home switch.

Or you can buy cartridge games and make them share.