FWIW...I wish I had a dollar for everything in my life that I've bought or built and then regretted it. Your yard has great potential for an interesting pool, with that large side yard, but the Pergola will have move (and maybe end up over the spa?) Be sure you know all your easement laws, though. Here, we have 7.5 feet on either side of the property line, or 15 feet if you happen to be at the perimeter of the subdivision.
Integrated spa vs purchased hot tub. The purchased hot tub will almost certainly be
functionally superior and easier to heat in winter than an integrated gunite spa. However, but as someone else pointed out, it will not help the appearance of your house or yard. Where a pool and integrated spa
may enhance your property and resale value, if you list your home for sale, the hot tub probably won't. Also, as a separate "pool", the time you spend taking care of your main pool water will be no help with your hot tub, which you'll have to separately maintain. My RE agent friend told me that first, a pool is a financial mistake (I knew that), and second, a pool without an integrated spa--at least in the greater Houston area market--is a double mistake (like buying a Mercedes with cloth seats.) I trust my friend, as every single piece of advice he gave on the preparation for sale of our last house was good. He listed it on Wednesday, had an open house on Saturday, and had two contracts on Sunday, including one at asking price. He also told me about a Texas property tax rule that no one else told me, including the local appraisal district or the "expert" property tax protest firm that handled our annual valuations. That tip now saves us $2,000 a year. When my friend talks about residential real estate, I listen.
Back to the pool. Wrapping around the corner into that side yard sounds spectacular. Having to move or remove the pergola just reinforces another suggestion my real estate friend suggested: Anything you do to your back yard--landscaping, hardscaping, swingsets, playhouses, storage buildings, etc.--should be done with a future pool in mind, even if you don't plan one now. You could change your mind, or a prospective buyer might want to be able to add a pool. Just one more opinion that's worth every penny you paid for it!

Good luck.