I just matched into derm this past match, and I was pretty surprised to learn that a few of the botox clinics in my city are owned and operated by FM doctors... in short, yes, but there are limitations. You can do Botox, Juvederm, etc... but there are a ton of things that are not covered in FM residency. If you only offer a few services, it's almost impossible to stay in business unless you offer extremely competitive pricing and market the hell out of your business. You can also choose to independently take courses and get certified in other procedures to expand your offerings. While you can start a business and do all of these procedures, you obviously can't claim that you're a board-certified dermatologist... there was an MD in LA who did his residency in I think ENT or something many years ago and he had a derm practice and claimed he was a dermatologist.. got shut down really fast. A surprisingly large number of patients are actually weary of the difference between cosmetic practices that are operated by board certified dermatologists versus doctors who are in other specialties, and some patients will not go to a doctor if they are not a board certified dermatologist. People that go to FM docs for Botox either go because it is cheaper or because they are not aware of the difference. I think from a business perspective, if you are operating a cosmetics practice and you are not certified in derm, this translates to not being able to charge as much/having a clientele that is significantly more cost conscious.
I wouldn't do family medicine with the eventual goal of opening a cosmetics office... there is a serious shortage of FM doctors, and that'd just be a waste of a FM spot honestly... I think as you get more clinical exposure, you will find something you're interested in. If you are interested in a lifestyle specialty (sounds like you are), I'd look into anesthesia or rads... Hours are super flexible and you can mold your practice how you want and still make a pretty buck. Anesthesia is not super hard to match into, and I think rads is getting less and less competitive. not entirely sure on that though.