This is more of an issue to be discussed in r/legaladvice since there are a couple different areas of law that are involved so you may have to deal with several different court systems to sort this out. I recommend speaking with a lawyer in your area too. However from what I am understanding it seems like you feel you and your SO are entitled to the home because you have been the primary caretakers of the property.

Basically (and I am not a lawyer so this may be somewhat incorrect depending on your local laws) as long as her father, your landlord, gives you ample notice before the sale for you to find a new place he is legally in the right as he owns the property. Depending on your local eviction laws and requirements for eviction he may have the right to evict you as you are merely tenants. So as far as staying on the property you may not have much of an option other than moving out since you are not legally the owner of the property. Caring for and paying for repairs does not necessarily give you rights to continue tenancy or rights to own the property if it was inherited by another family member. Belief he is selling to fund his habit is also not a sound reason to claim he is unfit to own the property as there is little you can do to prove that is his reason for selling the property.

In order to contest the ownership of the property you will most likely be dealing with probate court or maybe family court depending on exactly what your lawyer suggests. Inheritance is tricky if there is no will and depending on your local estate laws you may have absolutely no claim to ownership, but it really depends. If he was an unfit landlord and the property wasn't maintained in a livable condition by him you can possibly have a case against him for that but as far as ownership rights I'm not seeing any sort of legal claim your SO may hold on the property itself.

Personally if you are putting in more money into a rental property than the landlord, family or not, it is time to get out. You are spending more to stay in the run down property than you would be to rent a nicer apartment or a monthly mortgage payment. If your home is not livable and you have a child who's health is at risk living in that environment and you are content to stay there because "what the hell its cheap and convenient" then you have some serious things to reevaluate about your current living situation. I would have either moved out or reported your landlord to the housing authority ages ago. Which bodes well for them as you have never filed a claim so condition of the home before you moved in vs currently cannot be established unless you took pictures of all the original damage and have proof of infestation being prior to your tenancy from the terminator.