What do you do when your pets do not like each other?

Danyel, I have had similar situations before where one cat was deliberately picking on the other one, and sometimes that happens with dogs, too.
One thing that always worked for me was using a small squirt bottle. I would fill it with water, and then keep it close by where I could easily grab it when the agressive or playful cat pounced on the older cat.
Then , I would squirt the playful cat with the squirt bottle. Usually one squirt would be enough to discourage him, and make him run off; but sometimes, it might take several squirts, especially when they are wanting to fight with the older cat.

Once the agressive cat learns that attacking the other cat will get him squirted and wet; he will pretty much stop attacking, because he doesn't like being wet.
If just the squirt bottle with water doesn't seem to have enough effect, try adding just a little bit of vinegar to the water, and it will have a smell that the doesn't like, as well.