What exactly is the event that she doesn’t want you inviting people to?
Is it just a church christening, or is there a party involved?
I’m divorced, I organise my children’s parties. That includes doing all the catering, booking bouncy castles and halls, and paying for the whole lot. I actually do always invite my XH (it was fairly amicable) but after the first one he hasn’t bothered to come.
I absolutely would not want him thinking he could just invite people.
Now I know that a birthday is suddenly because it’s not a one off event - nothing stops the other parent from having their own celebration too, that’s quite normal. A perk for the children of two homes!
A christening is a one off. She absolutely should not tell you who you can and can’t invite to the ceremony. Not just morally! It’s a public event, she literally can’t.
But if she’s having a family and friends celebration afterwards, that she is organising, I can just slightly see why she doesn’t want you filling it up with other people.
To some people, a christening is a really important and meaningful ritual. Those people don’t usually wait until the baby is 15 months old, unless they are newly come to Christianity. To others, it’s just an excuse for a party. If it is just a family party, I can see why she wants that to be her family.
I think she’s wrong by the way. But say I was going to give her a 10/10 for unreasonable, I would actually drop it down to a 9/10, because I can see that to her, she might just want to have a family celebration without the ex and his parents.
If a christening is meaningful to you, then go to the ceremony. Invite anyone for whom the christening itself is meaningful. Nothing you’ve said suggests that the christening itself is. Personally, I was in your shoes my post would have been about her putting my child through a religious rite that wasn’t a religion I follow, without my permission.
Then arrange contact the next day / weekend and have your own celebration party?
But really... go and see a solicitor and sort out your contact. She shouldn’t even know if you’re inside or outside with your daughter. Or if you’ve been to your parents. How does she know?