Texas · The feature and the liability limit are different questions
A pool can be insured as property and still be the reason someone sues you.
“Attractive nuisance” is a legal idea about a hazard that draws children, not a line on your declarations. Whether you owe anyone is a facts-and-lawyer question. What the policy can do is narrower. Personal liability, often Coverage E, may pay a covered bodily-injury claim you are legally responsible for, plus defense as the form allows, up to that limit. It does not rebuild the pool. This is educational, not legal advice.
A fence, a self-closing gate, and a locked spa cover change the chance of an injury. They do not change the exclusion. Underwriting can also decline the house, or refuse the umbrella, because of the feature. An umbrella pays only after the underlying homeowners liability limit is used up. Carriers commonly want about $300,000 of underlying home liability before they will write it. That is an underwriting rule, not a statute. If the homeowners form excludes the trampoline, the umbrella does not sit on that loss. How the extra layer works: who needs an umbrella and umbrella insurance.
The rest of the form: what homeowners coverage is and Texas homeowners. The regulator: TDI.