Assuming this is a genuine post ????? Having personal experience of several thirteen year old girls I found they like nothing more than girly stuff, make up, fashion, music but it's not a competition about spending money, it's about giving time and not ignoring her because OH is manipulating her.
I would advise the OP to up her own game with the child, OH behaviour is not the girls fault but as you have been married for 12 years you have been around for most of her life.
Can you arrange a "girly day" , not necessarily pushing OH out but making more of an effort to be included.
As someone else has suggested, why not cook a special meal at home, get the child involved too and let her see that she is very much part of your life as well as Grandads.