I could've written that very same post myself not so long ago. Whilst I never wanted to see it as competing, the other GM certainly made it feel that way, and I don't mind confessing that I had a few upsetting moments.
Fast forward to now, and after deciding to let the other GM get on with being 'World's Best GM', I'm far happier, more content, and have a great relationship with my two little GDs (and also with my DiL, who, incidentally, is far more comfortable in our company than she is with her own parents!).
Now, when we have to be in the company of the other GPs, I just sit back and let them get on with demonstrating what being a hands-on grandparent is all about. They exhaust themselves by racing around after them, pandering to every whim, making sure they're eating, bathing them, putting to bed ... of course, they're far more capable of doing all of this than anyone else, and they NEVER have any problems with the grand children misbehaving
, just like their own children were always perfect and never misbehaved! They always take great delight in telling everyone this. Yeah, right!
In fact, I think other GM has now got the message that I won't rise to it, she doesn't impress me, I'm not willing to compete, and she can run herself ragged for all I care. I actually think she's now getting a bit miffed that she does most of the 'work' when we're all together, but that's what she wanted! Yet, GDs still come to me with their books, toys, asking me to play with them, etc.
We may not do the same things with our GDs, or spend the same money, or take to the same places, but our GDs still love coming to us, they love getting messy in the kitchen, and having the paints out (where as other GM likes to keep a tidy house!). And, they always give me big hugs, saying, 'I love you Nannie' ... without any prompting from anyone!
So, I know it's difficult, but do try to ignore the other GM, and just let her get on with what she wants to do. Just smile and nod in the right places. You'll develop your own special things with your GC, and they'll love you just for being you!