Rental Insurance Policy - Standard vs. Umbrella

[Darrick Lowe]

I have 2 rental properties (NY), but just have a standard rental insurance policies. I cannot get an umbrella policy with my current insurance company because I do not own a car. Do you think i am protected adequately as is? Is there a huge benefit to getting an umbrella policy? What are some liability 'holes' that I should be concerned about (ie. scenarios where I wouldn't be covered and my assets could be at risk)?

current liabilities per property are 1M business liability (per occurance), 2M annual aggregate, 5k medical premises payment. each 2bdrms with a couple and kid.

In addition, does anyone have any strong recommendations on insurance companies (e.g. allstate, statefarm, liberty mutual, etc) that have done well at protecting against tenant lawsuits? I heard that RLI offer standalone umbrella insurance