Can my ex legally drop me from her health insurance policy when she re-marries?

I am actually surprised that you are still covered if you are fully divorced; normally, a person may only carry a dependent child or a spouse (not ex-spouse) on the policy. It is almost certain that once she is remarried, you will be dropped; marriage is the sort of life event or change that allows changes to health insurance policies, and policies again generally only allow children or spouses to be covered--and once she remarries, she will have a new spouse.

If you have an agreement, such as via a divorce degree, that she has to provide you with health care, you may be able to force her to at least pay the cost (or most of the cost; e.g. up to the cost she was paying to have you on the policy) of your health insurance, even if she is not actually providing it.