I would guess with your daughter that she is looking to stress her own independence. My son pulls this even now, tho luckily, not as often as he did in that stage. We corrected it by ignoring it. I realize it's not easy to do when your attempting to get something done. However, I do offer my son choices - as soon as he was able to point. (So this started at about a year or so, he's now five.).
I feel that when we offer them specific choices, this helps to reduce those tantrums. It did for me, anyway.
I would pick two things out of what we needed and he was able to decide the 'final' vote. It still works for us!
I am a huge believe in choices and I feel depending on what you let them decide, it helps them understand the consequences of their decision - i.e. a specific toy they may want at the store, a type of flavor of drink, clothing - you name it. But it really does work once it's implemented. (Hey - little ones are people too, and should be encouraged to think and decide for themselves.)
As for Leapfrog toys - we have had only bad luck with everything we have purchased or had gifted to us. Nothing lasts, we had to purchase a new item to replace one that broke and it croaked as soon as the receipt to return it expired. I actually prefer V-Tech as these are also educational and we have items from my son being a baby. I truly feel V-Tech is a much better brand!
In addition, my son was actually very good to his Leapster products... He is surprising nice to his toys by not banging them, tossing or hitting.
(When he's not playing with his toys, I trust him on my computer on PBS Kids and Playhouse Disney. I have also found some educational websites designed for at-home teaching. I actually prefer that over gaming systems.)