Stop the project asap! If your Mother walked into the showroom, and walked out with a contract, that means the PB didn't even visit her home to view the site conditions. Any PB that would do business that way does not have your Mother's best interests in mind.
Have your Mother find 2 PB's (she should scratch the current PB from her list) who will visit her home, review the site, draw up a design, and give her a list of specifications including what equipment (brand and model) will be included.
Building a pool is not like dropping a hot tub in the backyard, and can't be treated as such.
It's a good thing you posted here, because it sounds like your Mother walked into the wrong pool store. Please let us know if we can be of any additional help.