A Liquidambar and a swimming pool cannot coexist in close proximity!! If not the root issues - which are significant with the liquidambar - then there is the issue of leaf litter and the seed pods clogging the pool and pool filter.

You have a very tight area in which to plant. Most suggestion are for at least a 6-8' distance from the pool for any type of planting. Have you considered a shade structure rather than a tree or shrub?

You know, you might be on to something.... maybe I could build some type of trellis with a vine flowering plant? But as I think about it more, this type of project would just add a large additional cost to an already extremely expensive project. I was hoping to avoid that. :/

I would remove the tree without hesitation.

Absolutely remove the tree or don't build the pool. Tree selection around a pool is tricky. I suggest you try the California forum for more regional input from Sacramento area pool owners who can offer real-time experience.