I don't manage to have my pets play, why? I tried two times with everyone.

If they're already as happy as they can be (having a Minion contributes to happiness) then they won't play. :)

well, I'll try to make them sad :-D

If your pets are in a resort, then they will be too happy to play. Also, it seems that some of my pets just don't like certain toys.. refusing to play but then willing when I try something new.

I suppose they simply don't like certain toys, as your pets, but this is a problem when I do major drills quest.

pets will always play with any toy if they're at all bored, and always eat any food if they're at all hungry. Their reaction to any item is just for color and it is completely random even if you feed/play the same item over and over again.

very interesting, thank you :-)

Actually, I don't think the resort affects happiness too much. Just take away the minion, and in a few hours, you should be able to play with them. At least, that works for me, and I keep all my pets in the Inn.