Ants are a fact of life. People have been trying for many years to "get rid" of them and in spite of the many products that say they will we still have ants, and often when one does either eliminate an ant colony or convince them to move (more likely), soon another colony moves in to replace those you just chased away.
Ants are not too fond of locations where the soil is disturbed often or too wet so some of both might convince them to relocate. Keep in mind that most any of the poisons that will "control" ants will also kill off the beneficial soil organisms.

Are these fire ants?

I'm not sure if they're fire ants or not. I tried to look up california ant species and the only ants with red bodies in there were in fact fire ants. However, it did say that they're non native pests and the area I'm in is unusually resistant to that sort of stuff. I stepped on one and it got very aggressive, mauling the thing closest to it and stabbing it repeatedly with its abdomen.

I understand that ants are just a part of life in the yard. I have many nests of tiny black ants in the roots of most of my oak trees. They're in the concrete walls of my garden. In leaf piles. I don't care about those as long as they stay out of my house. These red ants are different. They're very aggressive and my young children don't understand the meaning of "ants nest."

I went out to check on them this morning and they're gone, with the exception of a few stragglers. It's going to haunt me knowing that they're out there, in my yard where my children play, probably swarming under some foliage where I can't see them. :/

These are clearly not fire ants or your description of them would be much different; their stings are very painful.....and can be terrifyingly so for children. Plus, they leave very itchy pustules that can linger for days. "Bitey " just doesn't do them justice.

If there continues to be an over-abundance of these particular ants, or if they start to cause problems with the kids, you, or your home you need to capture a few in a glass jar (with a tight lid) and take them to your local county Extention office.

Do you know what Fire Ant mounds look like? They're different from what most people think of as an 'ant hill '.