Kids would likely come after the property after his death, claiming all kinds of things, it could get really ugly.

However, for more specialty risks (older buildings, recent claims, vacant coverage, builders risk, etc.) independent brokers generally can provide more tailored, better priced coverage. 

Insurance companies are in the business to collect premiums and pay the least amount (or zero) dollars on a claim.

She then took over the basement, locked us out of it,  and tried to claim it was hers, since she had a door from her unit that went into it!  

I've had people get mad at me claiming I am lowballing them or being greedy when the reality is we wouldn't stand to make much on that given deal.

They will just not pay for any claims you make, and if you already have insurance, that doesn't matter.If they did charge your card, call them up to cancel, or dispute the charge with the issuing bank.

If I were a property manager, I would want some basic liability coverage at a minimum to protect me from claims from both tenants (wrongful eviction, discrimination, etc.) and property owners (breach of contract, etc.).  

She claimed to have yet to receive any actual offers as of yet but there has been others whom are interested.

I know transferring title via quit claim deed can trigger "due on sale" however my question is if that happened could you just quit claim the property back the way it was to settle the "due on sale" clause?

This is not something for small claims court but rather a full blown law suit that will cost thousands and likely years at best if you intend to really pursue it.