They are already working on tweaking the minigames and making some optional :)
About the wolves, have you tried the "Polite Wolves" option? I'm not sure how it works since I haven't tested it yet, so can't say if it helps with the fence breaking.

EDIT: From the patch notes today:

Mini-games Enhancements:
* Enjoy instant milking in the milking minigame, resulting in one milk obtained. Speed and efficiency at its finest!
* Similarly, the shearing minigame now offers instant shearing, granting one wool. Your sheep will appreciate the quick and gentle touch!
* The saw minigame can also be completed instantly, offering one wood.
* Cooking UI has received a makeover! Now you can easily toggle between ingredients and recipes using the bumpers on your controller, making your culinary adventures even more seamless and enjoyable.
* Cow milking is now 30% faster, so you can efficiently collect that delicious milk without any delays.
* In the goat, horse, and firefly dream games, the rewards will now be displayed in the finishing window, adding clarity and excitement to your accomplishments.

It seems the key to the wolf dream is to have the dog bark. I've had a wolf run right by the dog when silent, but once I started barking as the dog the wolves all turned away quickly. Left mouse button causes the dog to bark on KB/Mouse setup - I don't know what that would be on a controller.

The other games haven't been too bad, mostly tedious once you have a lot to do, but I haven't gotten to the fishing one yet.

It's the A button on the controller.

There's something wrong with how the wolves work though. Depending on how you have built your farm there is nothing you can do to keep it undamaged. Even when I get to a wolf long before it reaches any fences, if I scare it away and it decides to run away in the direction I have a fence, it will still destroy all the fences in it's way, and then there'll be animals everywhere the next day. I tested just now, and I was helpless to stop the damage. One wolf appeared inside a pen and destroyed the fence when running out, the others destroyed tons of fences on their way away after I had chased them off, and the last one stole a sheep that I couldn't get to in time because I had many animal pens in the way and it was too far from where the wolf before that had appeared.

Normally I just skip the wolf dreams though so it's not an issue for me, and I'm sure they are tweaking how that works :)