As the mother of an 11yo girl I salute you both!
I try pretty hard (without trying to look like I'm trying hard) to encourage her to get out in the forest to ride with us. Success is relative - as in, sometimes it's better if you don't ride with a relative!!!
I have found my greatest success in getting her out on the bike in the forest is finding other girls of a similar age who also go out for a ride with their parents (Dads mostly). We have founded a very casual thing called "The Princess Rides" where anybody with a little girl can come and we trek across town to the easiest forest in Brisbane for a ride. They all seem to have a lot of fun and we work on skills - getting off and spotting them individually over logs and rocks and stuff. They seem to take to it much better without boys along who are much braver!
Also, one of the local race organisers who does our enduro races organises kids races during the main race - just a couple of laps around the marshalling area. All the kids get a prize and can tackle it at their own pace - or even have their parent ride along with them if they like. It really encourages them. My daughter has ridden in a few.
Keep up the encouragement - they need positive role models that aren't their parents!
