While the actual task I had to perform only took about 10 minutes, the carrier's website was acting goofy.

Find out if your existing Insurance Carrier will write a policy and include all the LLC's for coverage. 

I'd strongly suggest using an independent broker rather than a carrier or MGA like Steadily.  

Many carriers are seeing double digit rate spikes.

But, I know of a couple carriers who sell umbrella that will cover policies on multiple companies.

Until that is done, you should look for another Insurance Carrier that will write your home and extend Liability to that location or get a sepparate Liability policy to cover your wife's interest in the property.Once you have determined there is underlying coverage for the Liability on the vacation home, the question of the umbrella Liability (comes into play once the underlying Liability is exhausted). 

There are many Florida carriers that provide coverage designed for vacation rental usage.

@Roxanna Pifer This situation is common with insurance carriers. 

They have access to both the big reputable carriers, and the cheapo "good luck having a claim honored" ones.

Yes, There are several carriers that offer great portfolio master policies.