It does sound like you need to switch Lyme doctors, since yours won't treat him for Lyme or Bartonella. Did they ever test him for Lyme and coinfections? When it's this long-term and complex, there is always more than one infection going on. You can probably get LLMD recommendations on this forum if you start a thread letting everyone know you're looking for a Lyme doc in your area.
It sounds like your house may not be mold-free yet, and that is an absolutely essential first step. An air test won't give you a true picture of what's going on in your house. The ERMI test from Mycometrics is the best test, and if that comes back positive, it may convince your husband that more needs to be done. Also, there may be more to detoxing mold than just cholestyramine. Read the book Mold and Mycotoxins - Current Evaluation and Treatment by Dr. Neil Nathan. He treats different classes of molds with different binders including activated charcoal, chlorella, and bentonite clay, in addition to cholestyramine. These are things you could do at home without a prescription. His website is a great resource too:http://www.neilnathanmd.com/ I've spoken to him on the phone a few times and he is very knowledgeable and experienced.
Have you read about the ketogenic diet for siezures? I haven't researched this much, but have read about it here and there over the years. This may be something to look into, as it will simultaneously eliminate all the typical allergens others have mentioned - gluten, soy, dairy, sugar.
The picture you posted is definitely a Bartonella rash. We've started the Buhner protocol for Bartonella because despite years of treatment with antibiotics, our 17 year old still has it. He didn't have the rash to start, but developed it on his back 3 years ago and it's never gone away since. I know Buhner seems overwhelming, and I avoided even considering it for years for just that reason. However, there's a mom on this forum who healed her daughter completely with Buhner, and my brother-in-law is now having success treating his Lyme and coinfections with it. I would recommend just starting with his book on Mycoplasma and Bartonella, since you know for sure you're dealing with Bart. Once you read what he has to say, you start to understand how this infection works and why antibiotics are rarely enough. Even if you decide not to do his protocol, you'll have a much better understanding of what you're dealing with and may want to just pick and choose a few herbs to see if they help with symptoms. A lot of the herbs he recommends target inflammation in the body, and he explains why this is crucial to healing. We are planning to continue antibiotic treatment for while getting up to speed on the full protocol, as I don't think the antibiotics have been useless and Buhner even suggests that using abs AND herbs can have a synergistic effect. I've found the Buhner Healing Lyme and Coinfections Facebook page to be a good resource: https://www.facebook.com/groups/1441091676154216/
Also, I totally agree that heavy metal testing is important! Heavy metals can really wreak havoc on the immune system, and if your son was vaccinated, he is in the age range that received a large number of doses with the mercury preservative Thimerisol. Also, if you or he has amalgam fillings, that can definitely contribute as well.
I recently found a blog I really like called the Real Food Rebel: http://realfoodrebel.com/ She followed the Wahl's Paleo diet, not ketogenic, but I found a lot of useful information here.
Another great resource is the Better Health Guy blog: http://www.betterhealthguy.com/