Could I be liable for something that happens after guests leave my house?
In some circumstances yes, particularly where alcohol was available to minors. Social host liability is real and the resulting claim can be very large relative to a standard homeowners limit. It is one of the clearest arguments for an umbrella in a household with teenagers.
Does the umbrella cover my children?
Resident family members are generally covered, including teenage drivers, which is what makes one policy efficient for a whole household. It is worth confirming how a child away at college is treated, because that varies.
My teenager already made my auto premium jump. Why add more cover?
Because the premium went up for the same reason the exposure did. Cutting cover when the risk rises is the wrong direction, and an umbrella is a comparatively small amount of money sitting above all of it rather than raising each underlying limit separately.