Post Divorce - Child Birthday Scenario

My son's Birthday is coming up in a few weeks. He's young, 10, and in the past ( even during separation and before all of this ) his mother and I always went to dinner with him. This year is different. I've been dating someone for the last 15+ months and my child's mother is engaged. We went through a very long separation leading up the divorce however my son has been accustomed to week on and week off at our places.

My son wants to have dinner with his mother and me for his Birthday. I told him I will see him that morning when I take him to school and in 2 days after his Birthday when he returns to my home. He had some difficulty with that talk.

I'll say I have offered my son's mother the opportunity to meet my significant other and to meet hers. That would make this all a lot less complicated however this has not happened for reasons unknown to me. I think it would show my son that his mother has moved on and I have moved on but we still love him equally. My significant other has met my son numerous times and they get along and I believe my son gets along with his mothers significant other from what I'm told.

My significant other is not comfortable with me going to dinner with my son and his mom. She feels the boundaries are blurred. She also has gone through a divorce with children and does not have the same relationship at all with her ex husband. They rarely speak. When I do speak with my son's mother it's all about my son - black and white. Going to dinner with her ex and her children is not a thing and I respect that. My significant other is not controlling. She is analytical in thinking and we both share our feelings on topics openly and respectfully. She shared her feelings as it made her think.

Am I wrong for wanting to do what is in the interest of my son to show him we are being civil for his sake? Yes, I think meeting the significant others, prior to his Birthday, would have been super helpful and would make these scenarios a hell of a lot easier. My significant other is understanding and wanted to share how she felt about this scenario. I left it at that I would talk to my son's mother and invite both her and her significant other to dinner for my sons birthday with myself and my significant other. If my sons mother isn't comfortable with that I'll have to see if I feel up to just going out on my own and meeting them for dinner.

Post divorce - I am mostly good. These types of scenarios, like this one for my son's Birthday, I am not the best at navigating. Curious to see if anyone else has gone through this and where it led you. It does make me realize just because the divorce is done doesn't mean all the other things involving your child are done. That I know 100%. I appreciate any feedback that's left in positive light. I can take criticism too but be kind. I'm just a very good Dad trying to figure this out for my son's sake. Thank you in advance.