Does my policy cover a trampoline?
It depends entirely on the carrier. Some exclude them outright, some accept them with netting or a fence, and some do not ask. If the homeowners policy excludes it, your umbrella does not cure that, which makes it worth placing with a company that accepts it knowingly.
A neighbor’s child was hurt in my yard. What happens?
It is a liability claim against your household, and the limits on your homeowners policy and umbrella decide how it resolves. These are the claims that are hardest socially and most expensive financially, which is the case for carrying real limits.
Should I tell my insurer about the trampoline?
Yes. Non-disclosure does not hide it from an adjuster standing in your yard, and it gives a carrier an argument at exactly the wrong moment. Declaring it lets us find a company that will cover it properly.