I have 5 young children and apart from the first, have never really toilet trained the rest. The 3 year old had the occasional accident (only twice in the last year), and that was only because he was so tired, he slept right through without waking up for the toilet. My 2 1/2 year old son was dry during the day, but has now regressed back to wearing a nappy 90% of the time. I refuse to buy pull ups, not only because they are so expensive, but I don't see the difference between these and nappies. When I did try them, the kids didn't pull them up and down like undies (as you see in the ads). They just thought they were nappies with character pictures on them! And besides that, when I did have them, they purposly wet them (and not always when they were wearing them...I'm talking about under the tap) just to watch the picture fade.
Maybe for her grandparents, if the reason they prefer to use pull ups is because it's easier for them, maybe they could become her 'special' pants just for grandma's house etc. In any case, she will soon outgrow them and refuse to wear them. As someone else pointed out, kids usually toilet train themselves when they are ready, regardless of what we do to help them, and when that time comes, they will refuse to wear any kind of nappies.
(It's nice to 'hear' someone else call a dummy a 'binky'. Here I get all kinds of odd looks!)