Caro, should work for pet urine too...I've never tried it. I've refused to get anything beyond fish because I think I'd end up doing all the care!!
Flea, if she won't go at all in the toilet, then I'd suggest temporarily trying a reward system. A couple of Smarties, a handful of a cereal that she likes, a special mouthful, when she goes in the toilet. The reason a food reward is good here, is that they need something very immediate and very satisfying, but ALSO something that is quickly over. It doesn't have to be a lolly.
Also, again temporarily, a special toy to use or book to look at...just for the toilet. You need to encourage her to spend a little time sitting there. If she is sitting on it comfortably and relaxes, the position itself will encourage her pelvic floor muscles to open up and she'll release some urine.
Another idea...if the grandparents are really concerned, would they like to take her for a week and train her? If it's that important to them, let them try...after all, they have done it before I'm not being sarcastic, not completely anyway! Seriously, if granny is really keen to do it, why not? At your daughter's age, she should be able to learn very quickly if someone is there to remind her all the time, and if it's stressing you then let your mum or MIL have a go.

One thing to remember is that learning to use the toilet is just that...a LEARNED behaviour. Some mums think that it's a natural behaviour, like crawling or walking, and that therefore when the child is ready, he'll just do it. NO. We know, unfortunately from examples of abused and abandoned children, that unless it's taught in some way, it doesn't happen. Yes, they do have to be neurologically ready for it...but the neurological processes that are required, are actually completed quite a bit earlier than most people realize (usually by 18 months). I would respectfully suggest, just for future planning if it applies, that you start a bit younger...by age 2. The children are usually more interested and open at that age, less inclined to be busy and to say "no" to whatever it is you're suggesting! And if it seems impossible at that point, you can put it off for a bit and try again later, without feeling like you're pressed to do it by a certain time.
Fionajill, another thing some people try with boys, is to scatter a few Cheerios or Honey-Os (some small cereal that floats, these ones are rings) in the toilet water, and then get your son to "aim" at them. This is great for winter or wet days, or if you're in an apartment or other place where you can't have the fun of weeing outside!

Girls, after 4 kids and teaching many parents, I think I'd say this is not something to stress about...if it's driving you mental, use nappies and think about it next week or next month. If you work, I'd suggest waiting till you have a block of time off.
LOL, my youngest is a girl...I will be interested to see if there is any toilet training difference with her. I'm so used to doing it with boys! She just turned one and HATES being pooey. The other day my dh was home with her, didn't see her for a few minutes, and went looking. She was sitting near all the changing things, and gave him a great big grin when he came over--he said that, "Where have you been, Dad? Let's get on with it!" was the message she was trying to give!