Has anyone ever had their PTO denied?

I’m someone that barely takes vacation and I would always work and work. I have some family that I haven’t seen out of country since I was 8 and I’m planning on flying to see them this month in May. I’ll be gone for about 3 weeks. I’ve already purchased the ticket and just need to ask off. I’m planning on working the first three shifts before I leave (sun, mon, tues) and then the last three shifts when I come back (thurs, fri, sat). In between I would use 6 of my PTO to cover when I’m gone. I’ve just heard stories from other nurses that their PTO has gotten denied and I’m scared because I’ve already purchased my ticket. I’m planning on emailing my manager to let her know about my trip. What should I say in the email? What should I do if he says no?