This is kind of absurd. The point of on-call is not to have regular off-hours work, but to have someone available for emergent situations. Since anybody who intends to operate a service with constant availability must always have someone who can respond to emergencies, on-call is the system used by the world's most successful tech companies, not just two-bit upstarts. It's hard to imagine anybody serious about running any kind of online business who is going to respond to an outage on Friday night by saying "we'll look at on Monday at 9:00 PT." It's unfortunate, but it's really not that different from ER doctors, firefighters, utility workers, and numerous other workers working with similar constraints.

Besides that, the rotation is known, and planned for, long in advance. So your "long-awaited weekend trip" shouldn't have been scheduled during your on-call shift in the first place.