How bad is the mange? Generalized or localized? Obviously the dips are not working - and you're right, she probably is being over-exposed to the toxins. I'd find a new vet. Oral ivermectin is safer than the dip, and usually much more effective.
There are lots of threads in the forums on demodex and demodectic mange - a search should pull up some useful information for you.
Yes, mange is the sign of a compromised immune system - either genetically or caused by vaccination, illness, stress, etc. You can boost her immune system by giving Vitamin C, garlic, echinacea, goldenseal, and I'm sure other things I've forgotten (astralagus?). B-Naturals makes a supplement specifically for immune health, Berte's Immune Booster -
www.b-naturals.com Changing to a natural diet (or at the very least, although not ideally, a very high-quality kibble) will help; and she should not be getting vaccinations while she has the mange (even the vaccine manufacturers will agree with that!).