If I can hijack this informative thread briefly: how do you cope with her on hills joe? Do you run along in front/behind? Or just teach well and hope?
On roads, running shoes on, and I usually stay quite close to her.
On the really steep hill, I started off by holding the bars while she zoomed down it, and sometimes do still if she's tired or something. Nowadays she'll usually go down it herself, quite gingerly on the really steep bit, then shouting 'zoom' on the slightly less steep rest. I've taught her to stop at the side streets and only cross when I say, and to stop any time I say to stop.
I can just about run fast enough to stay in front, so traffic on cross streets permitting, I'll just run in front and tell her it's okay to cross, so she just keeps going all down the hill (unless there's something shiny and interesting like a slug, in which case we stop for a while).
I also bought a Chariot Trailer too which at the time wasn't cheap but it's proven it's worth in two years of use. Again, the cost may offend some folk but I'm happy with the amount of use it has gotten and the wee one is happy in it so why not eh? Someone has to try and prop up the UK economy
Adding up Rose's balance bike and her (Croozer) trailer, they cost about the same as my mountain bike. Which is quite a painful thought, but I'm still glad we got them. I reckon they've had more use in terms of hours than my mountain bike over the last couple of years - we use the trailer an awful lot, and she rides her bike most days, whereas I mostly ride the road bike.