Someone did say you can stick to aram in LoL or dominion but dominion is filled with bots at the casual level from what I hear, and arams does not a man satisfy. It's like just eating bread. Sure you can do it. It's just not very enjoyable.
My friends got me into both games tbh. I think also you should try to find something you can play with your wife, but maybe you don't need that much time together.
If you're going for casual 20 minute games, most games of hearthstone don't go over 20 minutes. I'd say 95% do not. But LoL and dota games can reach 1 hour at the 95%. If you're looking to unwind, the hearthstone community is amazing as far as TL communities go and the games are not stressful whereas LoL and Dota can really get your blood pressure up. You can't say mean things to people in Hearthstone either as the chat in game is just emotes. The worst thing about hearthstone is that many cards are hard to acquire without spending either lots of time or lots of money. The depth of the game is fairly low and while there's a lot to theorycraft, you can be gated by the cards you own. You can get pretty high in rank playing a rush deck or a deck with several rares after a few weeks of playing.
I recommend you stay away from MTG though. At least TL's MTG community. There's a few really hardcore assholes in there from what I've seen. MTG is lots of fun in person but you don't sound like you have the time for it.