Hi, and welcome to TFP. So sorry to hear you're having trouble with your new pool. Once you hopefully get past this snafu, we'll look forward to helping you with all things pool.
I don't think it's quite time to go full on lawyer mode just yet. If it comes to that, I can give you some thoughts (and you likely won't need a lawyer either way, there's a lot you can do as a consumer, now that you're in CA, that won't cost you much, if any). But first things first.
No, that is not normal for a pebble finish. I'm no expert, but my first impression is that the pebble was not installed correctly. There shouldn't be any cracks, and there shouldn't be any voids (like by the tile). No large chunks of white. And it looks to me like the plaster-to-pebble ratio is way off, as in: too much plaster and not enough pebbles. You should see almost all pebble, and little to no plaster. The "roughness" is somewhat subjective. It should match the sample you were presented, so you have something there. I, too, was disappointed in my pebble finish in terms of comfort. I used to have plaster, and pebble is considerably rougher. And while I think I got a decent job, mine can also take skin off if I rub hard enough the wrong way. Pebble is supposed to last longer, which, like you, is why I decided to go with it. I knew it wasn't going to be as comfortable, so I was somewhat prepared for the result I got. No matter, the finish should be consistent throughout, so if yours is demonstrably rougher in some areas than others, that is also a symptom of a poor installation. It's telling that he didn't want to install pebble, your result might be why. But a PebbleTec installer is supposed to be certified by PebbleTec, so hopefully your PB is certified and PebbleTec can be involved, as Kim suggested.
So what to do? My guess, with only your pics and description to go on, is that your finish should be replaced. If the PB comes back and says, in essence, that's as good as you're gonna get, or if he wants to do another acid wash (DO NOT ALLOW THAT), or if he wants to just drain the pool and sand/grind it smooth, I would say put a halt to any of that and demand better. Your finish should have met "PebbleTec Standards" from day one, and shouldn't need remediation after the fact, other than very minor defects. I don't think what you have is very minor defects.
You've already completed the first step, which is to let your PB know you're not satisfied. Is there any sort of time limit for his response? Did he say "I'll get back to you in a week." Or anything like that? Have you made your final payment? Give him a week or two to respond, but no more. DO NOT pay him anything if he is owed any money. You don't have to, for now, but we'll come back to that.
If it's been more than two weeks since you first alerted him of the issue, come on back and let us know and I can give you some "next steps."
If he comes back with "This is what we're going to do...", that's a good sign. But before you agree to anything, you might want to say "OK, I'll get right back with you on that..." and then check in here for some advice about his solution.
Here's what you need to know for now. It is common practice, unfortunately, for PBs and pool finish installers and manufacturers to try to blame you for any problems with the pool finish. One or all of those three may ask you for records regarding the pool's water chemistry since startup. How you answer that might determine your resolution, so be careful about what you say to anyone. Do any such records exist? They will look for any water-out-of-balance "proof" on which they can blame the problem, and then use that to void your warranty if they can show that you were responsible for the chemistry. Who has been maintaining the water since startup? That's a biggie. Let us know.
And the other potential problem is the use of the heater. You're not supposed to heat your pool right after installation. Was that ever discussed? Did the PB say that was OK, or not? Did you ask? Did you receive any "pool school" from the PB? Or a written set of startup instructions? Have you mentioned using the heater to the PB? You will need to decide about how to deal with that. I can't advise you to lie about that. But just be aware that if you cop to that, that could be "used against you." If the PB said it was OK to heat the pool, then you'll also need to decide if you want to get into a he-said-you-said situation, where you claim the PB talked to you about the heater, and he claims he told you not to, etc. Tough one. Just pointing out that what you say and can prove (or not) about how the pool was used and maintained in this first month can be used to void your warranty.
One tip I was given, and used, to get a very favorable outcome to my pool finish dispute, was to never say anything to anyone about the pool or what I did or didn't do. Only ask questions. Only answer questions with questions. If you get: "Did you balance the water correctly?" or "Did you turn on the heater?" or "Did you x or y?" You just raise your eyebrows and return a blank stare. "I'll get back to you on that." is the only statement you should make. Fire right back: "Are you supposed to be able to see that much plaster between the pebbles?" or "Are there supposed to be big white flakes?" or "Are there supposed to be cracks or voids in the finish?" Etc. Questions are not an admission of anything. Answers are. The idea is to get answers out of them, and not allow them to get any answers out of you.
If you cannot 100% limit your communications with the PB to letters or emails (that's what I did), then be sure to have another person with you for any meetings. Ideally someone not related. Avoid phone calls, they are the worst and virtually always lead to he-said-you-said arguments. If the PB tries to engage via phone, do not, just politely ask him to use email, or to meet you at the pool. As Kim suggested, any verbal conversations need to be followed up with an email summary of what was said.
The good news is, your pool finish should be backed by both the PB and PebbleTec, and you now live in a "pro-consumer" state, so don't panic just yet. You have a lot of recourse that could come to your rescue... Let's see what the PB says first and go from there. Good luck. Keep us posted and we'll help you all we can.