Is it acceptable to write several small papers that contribute to a larger paper? To keep this brief, I have two new math ideas that are supporting a larger work. I want to write two small papers detailing these math ideas (plus some other details I figured out about them), publish them to arXiv, and then cite them in the larger work. The smaller papers do not have enough substance for a journal or conference.

I want to do this because I want to provide details for the interested reader which are irrelevant to the larger work.

I am still new to this, so I ask: Is this acceptable? This feels like it might be unethical self promotion / self citation.
As you state it, you are probably going to be fine, however, you have a bit of risk. The first is that if the ArXiv papers aren't really "publications", then citing them doesn't really add much to your CV other than a bit of noise. 

The second risk is that a publisher has to agree that your "combined" work is still sufficiently novel to want to actually publish it and that is up to them and not a question that can be answered here. If all the novelty is already "out there" you might have a problem. This is less of an issue in math, of course, which has a preprint culture currently. 

An alternative strategy, that you can use or not, would be to write a good paper with the important results and then put the supplementary material somewhere that it could be found. 

So, ask yourself whether the combined paper is more than the sum of its parts for your reputation. It might be, or not, depending on the results.