Umbrella policy from different insurance carrier?

[Andrew K.]

I've got my primary home and cars insured with one company (carrier #1) but their quotes for my rental were twice as much as anyone else.  I received a reasonable quote from a second carrier (#2) just for the rental and I wanted to cover it with an umbrella from the first carrier.  Unfortunately the first carrier doesn't seem to understand my questions about if the umbrella will cover the rental even though they policies aren't all through the same carrier.  Can I assume the umbrella from carrier #1 will cover my rental if the policy from carrier #2 is exceeded in some way?  Should I look for specific verbiage in the umbrella policy documents (I haven't received any details just a a dollar amount for the $1M umbrella)

Thanks