If I keep the date and something comes up with my kids that night, doesn't that prove the guilt was right?
No. Children have needs that sometimes require you to reschedule. That's different from canceling preemptively because guilt found an excuse. Rescheduling when something real happens is parenting. Canceling before anything happens is the guilt loop.
How do I know the difference between actual parenting responsibility and the guilt telling me to stay home?
Actual responsibility is specific: a fever, a school event, a custody agreement timing. Guilt is vague: she seemed off, I should be available, dating feels selfish. If the need is real, you address it. If you're searching for a reason to feel safer, that's the guilt talking.
Won't my kids resent me less if I prove I'm willing to drop everything for them?
Children don't benefit from parents who model that romantic relationships and personal needs are things to sacrifice. They benefit from seeing adults who tend their own lives and show up fully—because staying home under guilt pressure doesn't make you more present; it makes you smaller.