(((hugs)))
Adwen, it's okay to be scared. You are in an unbelievably difficult situation, and you're doing amazingly well. You're going to get through this, and so will your son.
The best piece of advice I can give you is to speak to an attorney, not necessarily to start divorce proceedings, but to learn about ways to protect your share of the assets for you and your son. It does sound like your husband is about to go on a spending spree and feels entitled to do so. He absolutely needs to take care of himself, but he cannot unduly burden you and your son in the process.
I think that, when someone finally decides to transition, there is a sense of relief and euphoria. One feels a need to make forward progress. There can also be an element of healthy selfishness, because many of us have spent our entire lives conforming to the wrong gender and making ourselves sick in the process, all to meet the expectations of society and those around us. Transition gives us a chance to reassert agency over how we interact with the rest of the world, and that indeed can be selfish in comparison to how things were before, but that's not necessarily a bad thing.
That said, none of this is an excuse to behave poorly towards the people around us, and it certainly doesn't make us lose our ability to think logically. Your husband appears to have some underlying issues. They may be being made worse by the stress he is feeling about being trans, but they are independent issues, and if he doesn't work through them, they are still going to be there after he transitions. The impulsiveness and the selfish and controlling behavior with money (he's tight-fisted when you want to spend money on the family, but he's a spendthrift when it comes to spending money on himself, and your opinion seems to mean little in these financial decisions) will still be there. I hope for your and your son's sake, and his own sake, that he is introspective enough to work with his therapist to sort through these issues.
The electrologist to whom he is referring is probably Electrology 3000. They have a good reputation in the trans community, and your husband may be correct about going to them being more cost-effective in the long run, but that depends heavily on his travel costs. What is absolutely true is that going there requires spending a large chunk of money at one time, rather than in small increments as it would going to a local electrologist. If he hasn't, he should also consider laser, assuming he has darker beard hair (it doesn't work for people with blond or red beards). There isn't necessarily a right or wrong answer here, but you are right to be concerned about the financial impact, because removing a beard, regardless of the method, is usually very expensive ($10000 is an easy possibility).
Finally, I don't know what your therapist means in saying that your husband's gender specialist is "controversal." One thing you should understand is that there are often few therapists in an area that specialize in gender issues, so your husband may not have a lot of choice in who he sees. It can be hard to find good healthcare providers when you are trans because of discrimination and because, while the medical community acknowledges the medical necessity of transition, this is a relatively recent phenomenon, and most providers do not have sufficient training to feel comfortable dealing with trans patients and their specific issues. So your husband's choice of therapist may not be a reflection on him, but on the choices available to him.