Your mom wants to invite 150 people to a party at someone else's home in the name of good manners?
Also, if I got an invitation to a 1st birthday party to someone a plane ride away that I saw once every decade I would thibk it was a terribly tacky and poorly disguised gift grab, and a bad one at that since I obviously wouldn't be able to come and think that cake and ice cream with immediate family is the standard and maybe, maybe a pony at one birthday when you are 8 is ok, but nothing more than that.
I'm a old codger who thinks these kinds of things are now way way over the top, so take it with a grain of salt of course
