I think the obvious choice if you want something similar to BG3 would be the other RPGs from Larian. DOS:EE and DOS2:DE are both coop, both round based RPGs and can both be run on Linux. While DOS2 is definitely the better one of the two (and in fact the reason why Larian was contracted for BG3) it could be hard for the AM3, depending on the exact type. But even the first game is just a very good roleplaying game. From all RPGs in the Iso perspective I've played, I liked Larian's the most.

There are of course also the older Baldurs Gate games. Both are coop (if I remember directly, I'm sure at least about the first one), again both can be run on Linux and on old systems, since they are old games. Which is also there main disadvantage. If you're used to better graphics, gameplay, games where you don't just miss all the time and voice actors, these games just can't really stand a chance to the Larian produced ones.

Neverwinter nights should be able to be run in coop, but I don't know if it runs on Linux. Otherwise it has pretty much all the disadvantages of the old Baldurs gate games without it being Baldurs Gate. Pick any aspect of the game and compare it to Baldurs gate and it'll loose. What it has going for it, is the pure amount of fan made campaigns for it. So if you and your kids like playing it together, you won't need to stop any time soon.

The only other "real" RPG coop campaign in my mind would be solasta, but I guess this would be too much for the budget PCs.

If you go away from the pure RPGs, there are some more options. Borderlands 2 can be played completely coop, has a pretty timeless graphic which is still easy for most systems and can be run on Linux. But while it has one of, if not the single best villain in gaming history, it's technically a loot shooter and not an RPG. Even if one of the DLCs literally is a DnD campaign of the characters.

Relaxing the RPG theme further, we see some more options looking at indie games. Games like Stardew Valley or Terraria are both simple, can be seen as RPGs by some and come with multiplayer. Both are very famous and not without reason. If the other games don't work out, they are a good option for everybody to find something to have fun with.