Why does the mother have to announce to the world how wonderful and thoughtful she is because she's donating money to a charity? Why does anyone have to know this?
Is it mandatory in your social circle to spend X amount on a child's birthday party each year? I don't get it. It's nobody's business but mine if I have a birthday for my kid and how much I spend on the party.

I wouldn't go around telling people I'm cutting back and giving what I would have spent to charity. Who would care?
Why not forgo the party all together and donate all the money to a charity and not tell anyone you are doing it? Why does anyone have to know what you do or how much you give?
It all goes back to tooting your own horn and letting everyone know how great and generous you are!
I'm waiting for the day when I receive a non-invitation in the mail.
"You would have been cordially invited to attend _____, however, we have chosen instead to donate all of the money to XXX charity in lieu of spending the money to celebrate the occasion with you. Although optional, gifts will still be appreciated."