You sound strong and I like your idea of a family birthday meal and you baking a cake. I know that being part of happy family times was a major component in my H not leaving when he had his PA, 8 years ago. He later said to me that he just couldn't trust that our children would remain as happy if we separated, even though OW was trying to convince him that they'd be happier since he'd be happier with her. At the time, he agreed that he would be happier with her but he couldn't quite picture the kids getting along with her the way they get on with me--especially S13 (then S5 who loves the smell of my hair).
Since your H has texted about how much his boys mean to him, I'm sure that he is very sensitive to how precious the times are when you are all together happily. He is bound to realise that staying put as a family is the setup that is most conducive to his sons thriving. I really think you can capitalise on that (without mentioning it obviously).
Anyway, all this to say that an H can recommit to his M initially because of the kids, not because of the R with his wife. If you have any doubts about your H perceiving a dinner out with you as pressure then definitely go for the family birthday celebration. I think that can be very powerful.
While the info you've found out about your H and OW(s) is painful, I do think that it can motivate you to be an even better DBer. Not knowing that there is 'competition' puts you at a huge disadvantage. In my sitch, I felt that I had started late in the game whereas OW knew that she was trying to seduce him away from me. Once I knew about her, there were times when sheer competitiveness motivated me to carry on DBing. I was d@mmed if she was going to 'win'. Sure enough she started giving H ultimatums that stressed him and ultimately pushed him back towards his family.
Keep us informed and good luck!
Me: 51 H: 52 T: 23 yrs M: 19 yrs S18, D16, S14 (special needs) PA: 2003/2004 Piecing: 2004 on Suspect H had EA: 8/2012-12/2012