This is an awful thing to say, and on that basis, YABVVVU. You don't have to understand her lifestyle choices, just as she doesn't have to understand yours.
You know that you're allowed a hot tub. You also know that the hot tub is noisy and irritating.
A reasonable person would appreciate that their choices were impacting on someone else, and time their usage to minimise the disruption. If you don't know when that is, ask her.
All you have to do is say with it getting warmer in the summer months, your kids are going to spend more time outside and you're aware noise can sometimes travel - are there any days/times which are particularly better/worse for her, so you can try to work around that when you can?
It's not a promise you'll be quiet all the time. It's an acknowledgement that you're upsetting her, but that you'll do your best to annoy her less. If she knew you weren't deliberately trying to wind her up, that would probably in itself make her feel better.
For all you know, she's studying for a degree at home and she can't think over the noise. You shouldn't be quiet all the time, but if you know your neighbours work from home during the day, do shift work, study from home, anything like that - you try your best to work around it. You can't always get it right, and your neighbours shouldn't stop you from living your life, but you should always try to be nice where possible.
I mean, who wants to live next to someone who hates them? You try to get on with your neighbours as much as you can for an easy life. When you fall out with your neighbours, things can escalate...