Friggin' environmental nuts. We should feed them all to the cats. Who in their right mind fights to introduce a man-eater to areas frequented by families?!?
Environmentalists.
Oh, you said right mind.
*nevermind*
"Any suggestions? Keep them close, behind and carry?"
Some here may disagree with me but I was raised rurally and I will not go into the woods without a gun. Wilderness IS beautiful but it also can be very dangerous.
Actually, that question can be reversed and be just as true. If a mountain lion attacks you in the local park in the middle of a major established sub-division the way you worded the question is accurate, but the key thing to remember here is that there is a reason why it's called a mountain lion, and not a mall cat or a lounge lizard.
Have a family discussion. Explain that fighting back is good.
Hit the predator with everything and anything handy. Try a rock or just your fist to their nose if they come that close.
Do not let the eco-nuts keep you out of our public lands. They try to convince us that it is government land aka no tresspassing "wilderness."
Forest land and BLM you can carry a weapon, but generally not in a federal park. Get some good range time and/or training if needed.
Bear Pepper spray can work sometimes...sometimes not.
Making noises (loud whistles) can sometimes be effective.
Have a buddy system for the kids and/or an adult near by. The kids will learn alot ...so go.
The best thing to do is to keep the kids close to you. If they wander away, they will be more likely to be attacked if a lion is stalking your family.
However, your actual, realistic odds of ever having a problem with a mountain lion in Colorado are somewhere on the order of one in a billion. If you'd like to worry about something, I would worry about getting into a car accident on the way there, or sunburn. My total mountain lion experience in 30 years of living and hiking in the area is that I once saw a footprint.
While I think you're right to be prepared and to think about this, and I know you've been given advice already, I would quibble a bit on the detail of 'ahead' or 'behind'. I ride frequently through cougar country on my horse, and while I've never seen one, I'm told if there was ever one around, he'd be tailing behind me and just out of sight. IOW, they'd likely be tailing you. Just keep the kids close, both for cougar threat and other risks.
In bear areas, encourage the kids to make a lot of noise and talk loudly where rounding corners where a bear may be surprised. In areas where there's heavy cover, bears are likely to be walking right down the trail looking for berries.
That said, go - and have a good time. Most of us spend years in the woods and never see a big predator, in areas with a healthy population of hunters they are still wary.
Keep them close, IN FRONT and carry?
A cat will generally attack from behind. If everyone walks with just a broom handle as a walkingstick/weapon you'll probably be OK. Myself, I would have a revolver under my vest, just to make noise you understand.