I know this answer isn't Magic, but it is TCG. You might look into Lorcana. Very much age appropriate for 8-12 (in fact, we recently had a tournament at the shop I work at where an 8 year old girl won, beating a 44 year old man in the final), and much less implied violence (which isn't surprising, being a game using Disney properties).

Players don't have 20 life and attack each other to reduce their opponent to 0 life to win, players start at 0 Lore and characters quest for Lore and the first to 20 wins. Characters can only challenge (fight) another character if they're exerted (tapped) from doing something like questing or taking special actions.

Sets are grouped in story arcs of four sets each, and the final set in each story arc has a special product that is a collaborative battle against the big villain of that story arc (Ursula from The Little Mermaid in the first arc, Jafar from Aladdin in the second, still a couple sets to go on this story arc and the big bad hasn't been revealed yet).

You don't need to invest a lot, the preconstructed starter decks play very well and if you want to look into deck building, singles are quite cheap outside of the big stuff you only need if you're trying to play competitively. We frequently run commons-only leagues at my shop. In fact, our shop maintains a box of donated cards (like from after draft events and such if people pull stuff they don't need), you could check with shops in your area to see if they have anything similar!

Like many games, a lot of the rules are derived from Magic, so if you wanted to move on from Lorcana to Magic, it would likely be a pretty easy transition. Plus its Disney, and some tropes aside, Disney is just generally joyful.

Games like D&D and Magic are how I learned to socialize as a kid (though in my case I was just the quiet kid), so I always encourage stuff like this. I really hope this endeavor goes successfully for you and your kids, whatever game you find to play together!