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I do believe they can live to be a few hundred years old. What symptoms are your trees exhibiting?

If your referring to the California Pepper Tree, yes it most certainly could have roots invading your pool area.
It's root system goes everywhere and anywhere to search for moisture.
It has a surface roots and the roots are invasive and have caused problems with breaking pavement, invading sewers and drains.

I would have your situation looked at by professionals to determine a course of action.

Hi Cheryl, Pepper trees don't produce legume seed pods like that. I believe what you have there is mimosa (silk tree, Albizia julibrissin), very common in your area and a very good tree for the climate. You can try to propagate from seeds, but if I were you I would buy a desirable variety from a garden center. There are some good nurseries in that area.
If you really want a pepper tree, you need to differentiate which species. Peruvian pepper (aka California pepper, Schinus molle) is also a great tree for Danville area, as is it's cousin Brazilian pepper (Schinus terebinthifolius).

https://www.google.com/search?tbm=isch&q=mimosa+seed+pods&chips=q:mimosa+seed+pods,online_chips:albizia+julibrissin&sa=X&ved=0ahUKEwi1h5aL5vvcAhXEZt4KHYIkA4cQ4lYIKSgF&biw=1280&bih=626&dpr=1.25

Unfortunately, none of those options will help with the issue at hand. You will need to find out what the exact problem is to know what you need to do to correct it. I can help you to find out what that is, but I will need quite a bit of very detailed information about the damage or issues, and most importantly, Photos!

There isn't really anything that you can do to keep them from growing, and especially with this tree. Even when they are perfectly healthy, they will sprout suckers. The only good way to deal with them is to keep them cut, unfortunately.

Here are some articles for more information:

https://www.gardeningknowhow.com/ornamental/trees/pepper-tree/california-pepper-tree-care.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-sucker-removal-and-tree-sucker-control.htm

Usually, larger roots can be taken out, safely, as long as you take extra measures to prevent rotting, afterwards. Do your best not to disturb any other portion of the root zone to avoid too much stress to the tree.

I would recommend adding beneficial microbes to the soil, since the leading cause of death from cut roots is rotting. Beneficial microbes will help keep pest microbes out of the area.

https://www.gardeningknowhow.com/special/organic/biofungicide-information.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/do-soil-microbes-affect-nutrients.htm