When she arrived, I would have said something along the lines of,
'Hello Jane. How nice you could make it. I didn't think you were coming because I hadn't heard from you. It's really good you and Tommy are here now but because I thought you weren't coming, I haven't sorted out a party bag for him.
I'll have a word with the magician and see if something can be sorted out. If not, you might be able to organise something with him later.'
That way, I would have let her know that the fault of the missing party bag was hers but without being bullish about it or making it look as if this was a big drama. She would have got the point and I would have not lowered myself into looking as if I was a person who got wound up over a child's RSVP.
As for the pizza, I would have done what any reasonable person would have done and tried to accommodate the child.
'Thanks for letting me know Tommy is a vegetarian but I had no idea about that. I can make him a cheese sandwich or I can try to order in a vegetarian pizza or you can do it if you want to be sure about what he eats.'
Again, making the point that she was at fault for not letting me know this either but not lowering myself into being the type of person who is thrown off course by having to order an extra pizza.
Regarding your husband's involvement.
My husband is a charming, well mannered, professional and well educated man so it is difficult for me to imagine him becoming embroiled in a row over a child's pizza and party bag.
However, if he had so little to do that he needed to place himself in the centre of a row about a child's party, I Imagine the last thing he would be doing would be contemplating telling Jane to 'fuck off' in the school playground, even if she approached him.
If he did, I would be ashamed not proud. I would also be very wary of anyone who, like your husband, says that they don't care what anyone thinks about them. That may be a recommendation in your world but in mine, it most certainly isn't.