I understand. I hated my frizz and wanted to relax my hair too. Been there, done that. Not the relaxing, but the hair loathing. Now I don't have much frizz if any. I get a little in the mornings when I wake up with is easily fixed/soothed and a little when I exercise or move around that's also super fixable. I realize the majority of curlies will always have frizz to some extent but most people here will attest they were able to get rid of the bulk of it just by learning how to properly moisturize and style their hair. It might just be your product and styling regimen that's keeping your hair from looking its best. If I tried to style my hair curly before I usually had lots of frizz at the canopy and bushy waves that turned into curly tendrils a quarter of the way down, similar to yours although I don't think your hair looks as bad as mine did back in the day. Yours is actually quite pretty and those pictures are nice. It's a sign your hair isn't so damaged from the styling it straight.
So first off I think you mentioned Head & Shoulders shampoo. I have to warn you I've heard such bad things about Head & Shoulders and how it can actually create more dry scalp and drier hair than help it. If you're going to switch one product in the shower, I recommend switching to a gentler shampoo. Next too many products (especially hair serums that are full
of silicones) will leave your hair feeling gunky, even if it doesn't look it. I personally detest moose in my hair. It also has a volumizing effect and hello, I've got a lot of hair, a lot of poof, what do I need volume for? I suspect you just need a good leave in and a decent gel (since your curls are loose and need protection in order to not lose their shape.) You also need to implement a few things to encourage your hair to clump into pretty ringlets, which will help with volume.
For instance, make sure the last time you run a wide-toothed
(so important! but I'm sure you know) comb through your hair is when you're in the shower, with conditioner and your hair is sopping wet. That's the only time you ought to detangle, and you should do it gently if you can. When you get out, try putting a light leave in. A bit of your regular conditioner should suffice. You want your hair to have the consistency of seaweed. Smooth it on. Then you can either put in gel when your hair is sopping wet or damp. I prefer the latter for me. My hair dries very quickly anyways so more often than not I don't have a choice. (My hair is high porosity so even though it is thick moisture leaves it quickly.) I smooth the gel on and scrunch it up. In between my leave in and gel I tend to scrunch out excess moisture with an old t-shirt. . . Maybe I mentioned my general routine before. I'm not sure. The reason I bring up reducing volume and poof again is yesterday I tried an experiment in which I raked in (finger combed) my products post shower. No dice! It was so not good. My hair was huge again because my curls were too skinny. In order to reduce volume you've got to let your hair clump. Honestly my hair is typically half even a third the size it used to be.
As for the reason you asked, I think you were just curious about people's experiences in general regarding relaxing. I'm sure any women out there who did have a good experience relaxing are probably hanging out on a different site but
there is a section here in the curltalk discussion board about retexturizing and relaxing that you can go to. I'm not sure how active it is but I'd go there and post because women are probably knowledgeable and they'll share what worked for them.
If you really want to wear your hair straight, I recommend you keep flat ironing. It's not so bad actually. Use a quality flat iron, try to keep out of the 400 degree zone (although I never followed that rule. . . which is why my hair might be worse for the wear), and always
use a heat protectant. A light hair serum which you gloss on the surface of your hair afterwards should keep the frizzies at bay. Then try to go at least three days before you flat iron again to prevent excess heat damage. Get a roomy shower cap so you can shower and not get your hair wet and mess it up. Be super careful when you exercise. Clip and pin it up. I would ice drink water during my workouts so I wouldn't get sweaty while exercising and mess up my hair. Also get regular trims to cut out old damaged hair and keep the cycle going. . . So 45 minutes straightening every few days, it was okay for me. It's just easier curly.