In my circle of friends and family, asking everyone to chip in $175 for a birthday party is flat-out batshit crazy.
I mean, from the tone of the "invite," it sounds like they were trying to do the right thing, throw a nice shin-dig for Granny but really has no idea what they're doing. (And/or did it at the last minute.)
My response would be, "Dear Sister, No fucking waySorry, we can't make the party on that day, but we're planning to swing by Granny's place a few days later and spend some quality time with her then. Toodles!"