I remember last year when my daughter was learning to ride solo without stabilizers. So due to nervous, slow and wobbly nature we took her on a cycle path (Bristol-Bath) away from fast motorised traffic. I won't forget the fear/panic caused by the occaisional cylists rushing past at 20mph with inches to spare. Shouting a warning can makes things worse as it startles/scares peds/kids.
Cylce paths are shared facilities, and kids and pedestrians have every right to use them. Slow down be polite and pass safely. If you want to ride fast and not have to clown as much then find a main road.
Your young daughter is also quite legally entitled to be and feel safe on the road too. The fact that you think that a cyclepath is needed shows how bad the situation on the road is. I could easily pass your daughter riding at over 20mph on the road, and give her a very wide berth and not make her feel threatened or intimidated.
But, on the cyclepath, I would have to slow right down. I'd also check that she wouldn't steer into the part of the cyclepath I would ride on while overtaking. It would need some thought before overtaking. If only all motorists drove like that, we wouldn't "need" these cyclepaths.
Also, cyclepaths are nothing more than legalised pavement cycling. I ride on them like I would (but don't) ride on a footpath. I cycle past schoolchildren on my daily commute on a cyclepath (It's that, or wait for several minutes to make a right turn onto a busy road, so no real time difference) I always have it in mind that pedestrians don't watch where they are going. The children run all over the place. I just watch them. They can be good entertainment if you have the right attitude. I think that they see me as a smiling and happy cyclist, rather than an angry cyclist who is always in a rush and full of self importance.
As Andy G says.
You just gotta chill if you want to use the cyclepath.
Or you can always use the road if you're in a hurry.
