Awesome adventures with your kids! How old are they to be that active? My little girl is 5.5 and she is spending several hours each day on her bicycle. I'm about to get her out on a wide trail. Kid #2 will be here in a couple months!
In the photos my son is 12 and my daughter is 9. I have another son who just turned 6, also. Living in Southern Cal provides the opportunity to explore nature, from easy hikes to really difficult stuff. For example, just 2 miles from my house is a nature preserve that allows for miles of pretty flat hiking/biking on both fire roads and single track. My oldest began biking the preserve with me when he was 5. Of course, my daughter wanted to join as soon as possible, so she has been riding since about 5, also. I have found that once my kids can ride a bike with 20" wheels and gears, they are capable of some trail riding. In fact, my youngest just joined our mountain biking since Santa crought him a new bike!
My daughter's first real test was when she was 8. We were car camping on the eastern side of the Sierra Nevada @ about 9'500' and I hiked her up to 11,500' over 5 miles. That was a long, challenginf climb for any 8 yr-old. Of course, there was some cajoling on my part..."It's just a little bit more"...and, "Let's go another 15 minutes." Soon enough, we reached the pass, and once my daughter saw the other side, the wide expanse of meadow, streams, and lakes, she was so amazed that she announced on the spot that she wanted to go down there! Of course, we didn't that day because that would requires backpacking, but that's what I wanted to hear!
My tips, allow for many breaks & SNACKS. Other than that, nature is so invigorating: snow in the mountains in July, streams, lakes, etc. One last tip, my daughter loves ice cream, so every time we return from something strenuous, I always treat her with ice cream.
Sometimes, I have to push my kids a bit, but they have learned that there is nothinng like a summit, alpine lake swim, secluded beach, etc. I have always planned a destination with a view, and my kids now take pride in knowing that nobody in their entire school has experienced the views that they have. Ha ha!
My youngest can only go so far, so you don't see him in the photos I posted, but he is just too young to pursue the strenuous hikes. He still loves to run all over nature, without regard to its inherent danger. He's learning, though, and it's all a blast for me to witness.
Enjoy these times with your daughter and, hopefully, she'll be ther with you doing something you both love!