DD2 will soon be 2. I suggested getting one of those micro-scooters (2 wheels at front) but DH thinks a no pedal bike would be better. We live on a fairly busy road so probably bike would be better otherwise will constantly have battles over her wanting to scoot down teh road and us definitely saying no.
I'd think with either, you're going to have battles - welcome to having a two-year-old! (That being said, my DS2 has never tried unreasonably to bike on the road - he only wants to bike on the basically unused road near us.)
I've always used the no-pedal bikes, and been happy with them. Two isn't too young, imo, but you might need to check carefully that the model you get will fit her, iyswim.
2 is fine for a "no pedals" bike. We bought a wooden like-a-bike and have used it loads, it is very light and I find it as easy to carry as the scooter. They can go quite fast on the bike once they get confident so be prepared to run to keep up. Definitely helps with balance and for riding big bike without stabilisers ( although most kids manage that in the end anyway)