One possibility: see the opinion of R. Raphael Saffra cited in Shoshi's answer about the Tablet-K hechsheranswer about the Tablet-K hechsher, that cheese made without real rennet is permissible. While this opinion isn't generally accepted (and indeed that's why, as mentioned in that answer and several other ones, neither is that hechsher), perhaps that might give you halachic wiggle room to at least eat other kinds of food made in your family's pots and pans, even if not the cheese dishes themselves. (As you've already mentioned in a comment on the question, this is of course something about which to consult with your rabbi.)
You mention in that comment also about dishes that haven't been used in 24 hours. Provided that there is no visible food residue left on them, then indeed halachah considers that the taste of the food molecules absorbed into the dish is pagum ("impaired") and doesn't have the same capability as before to render food treif. This can get pretty complicated, though, and I don't know whether washing the dishes during this time (in hot water, naturally) resets the 24-hour clock; but again, that's something for a rav to decide.
In any case, I wish you hatzlachah, and an easy time of it, in your Jewish journey!