Look up how to block installs. There’s a number of ways so you need to decide what works for your situation.
Or get your wife her own phone and let her deal with it.
There’s a few things you can do here… from easiest to hardest…
Like everyone said, teach your wife to be a more careful user
Tell her to get a Google Play Pass and play those games only. It’s Google’s subscription service that provides a few hundred games, all Google-vetted and free of ads and in-app purchases. They’re typically excellent games in their own right, but these special versions (exclusive to Play Pass) are much less intrusive. Everything is included with your subscription and they don’t bug you to buy anything else or watch stupid ads.
Get a systemwide ad blocker like Adguard. That will stop many, but not all, in-game ads. If you enable HTTPS filtering, it will block a lot more of them (but still not all).
Make her an Android Private Space and tell her to install the games into that private space. That way they will be sandboxed, completely stopped as soon as she exits the private space, and can’t spam her with ads and notifications the rest of the time.
On second thought… maybe #1 would be the hardest? Depends on the specific wife model and version