That's a pretty good understanding of it. Basically, what happens, is that the EMDR allows you brain to reprocess the traumatic situation during REM sleep.

After a few nights' rest, the trauma is lessened. I'm sorry to hear that you've had fatherly troubles, too. I hope your EMDR is successful, but it sounds like it will be! The only thing is, if you have sleep apnea, it might not work. My mom got EMDR done, but she told me that it didn't do anything for her. I think this is because, at the time, she had undiagnosed sleep apnea, and she was always waking up because of the stopped breathing and she never went into REM sleep... Good luck!
-GatsbyLuvr1920-