I understand your discomfort, but chances are your kids will call her what their cousins are already calling her. I think it will make everyone uncomfortable if you try to force the issue and have your kids call her something different.
Agreeing with this, but also pointing out it'd be awfully confusing for your kids-to-be, and any other relatives, (if you are near enough to eachother to have the usual big family gatherings) to be calling grampa's girlfriend a different name.
My son was the first and he dubbed my mom "Gammie" because he couldn't get the R in there. (He named my step dad Boppa.) My neice, nephew and daughter all came along, they were Gammie and Boppa.
My next neice and nephew came along and my bro/SIL said it had to be Grammie, not Gammie, but Boppa was ok.

It gets very confusing with some saying Grammie and some Gammie. (And to make it wierder, my gram is often there, and everyone calls her Grammie....)
IMO, it's just going to be easier to go with the names already in the family. You could always do Grammie Last Initial to differentiate since they have the same first name.
(You could also have some wierd other thing your kids make up- my kids refer to my dad as "Grampa by the Lake" even though he sold that house about 10 years ago, lol.)