I just wanted to share a story with you about annulment from a child's perspective. My post-college BF's parents divorced when he was young, and his father pursued and received an annulment through the Catholic Church. It really affected him and his relationship with his father as a young adult. He felt that his father was somehow saying that their family wasn't real, that he and his brother were illegitimate in some way. The annulment was more impactful to him than the divorce itself (in his head-- obviously, the D was the big thing, but a lot of his trauma centered on the annulment). It represented, to him, a level of rejection from his father and he had a difficult time wanting to or trying to be close with his dad because of it.
Just one story, I'm sure there are many others with other perspectives. This just happens to be the only person I know whose parents' marriage was annulled and it really affected him into adulthood. I know you are a great dad and love your children very much, and if I were in your shoes I'd just want to think about the long-term effects of pursuing an annulment on your kids.
Sounds like you have a great weekend in the works. Have fun!
May
Me (46) H (42) M:14 T:18, D9 & D11 4/19 - 12/19: series of escalating BDs 9/20 - present: R and piecing