Honestly, even if it did have some impact on customer or company, that’s clearly justified time off (although I don’t think you should have even had to take annual leave for it but that’s another conversation/issue).I once had to call in first thing in the morning and take a half days holiday to take my cat to the vet after he'd been hit by a car. My manager berated me for it for weeks, how you can't take holidays at such short notice! She was a childfree cat owner like myself as well but zero empathy.
Edited to add: i work alone in a role where me taking that half day had no impact on anyone else at the company or a customer.
Hope your little one was ok