What is the existing age of the finish, finish Type and condition? You should ask for cost of full chipout, but don’t be surprised they state they don’t do. Some contractors will say no, then later say can but cost prohibitive. Full chip out is not standard practice in Texas unfortunately. Same family own company performs full chip out standard in CA and NV, but not TX. Depending the condition of the existing finish and if original, a sand blast may be needed (many will offer sand blast in leu of full chip out.) Full chip out or very high pressure water blaster to remove finish to gunite is ideal.
1st quote looks standard stop by the house. Most likely followed up with details at the shop with tile, coping, finish details before signing. Second one is very quick here is the price call us if interested.
for who ever you choose, ask for references and go check out their workmanship on several pools varying in time work completed.
cd