You've stated that your sister-in-law has been unwilling to increase the insurance coverage. You mention that you're currently attempting to arrange a partition sale. You haven't stated whether she's willing to work out ownership issues voluntarily outside of a courtroom or if you and your wife are pursuing a judge-mandated partition sale. You also don't outline who is currently living in the home or whether it's considered a business rental property that has tenants or possibly a vacant property.
As you've already seen to a degree, insurance coverage relies on a variety of factors related to ownership, such as the policy owner and the owner of the property. Who currently lives at the home can also factor into decisions related to insurance coverage. Given that the property now has three owners instead of one, you should speak to the current insurance company and several other insurance companies in that specific geographic area about your situation. You should also speak to a local estate lawyer.
It sounds like the current insurance policy doesn't take into account the existence of three owners. This is a problem since the insurer likely requires that a new policy be written when there are ownership changes. Although the existing policy names only the one sister as the "named insured," she might face difficulties in the future if she tries to make a claim. An insurance company will typically print a check on a valid claim in the names of all owners when a property is owned by multiple people except for in certain special situations.
The important thing is that you don't need to be on the policy to ask generic questions of the current insurer to determine any requirements that it has in general for homeowner's insurance and liability coverage that involve multiple property owners. Speaking with agents from several companies then gives you more information in general regarding their experiences with this type of situation that you can use to compare with what the existing company tells you. Lastly, a local estate lawyer will have experience with this type of scenario and can better advise you on the best course of action to take given the implied insurance and property sale disputes.