One of your big obsticals will be properly outfitting them to be comfortable outdoors. My kids are costing me a lot this way. Boots, jump suit, snow suit, jackets, cam iackets, tain jackets $80 each. Hats vest and gloves 20 bucks each. So find a source for used stuff and keep a sharp eye out for used stuff. Don't cut cost here, your kids need to be comfortable to enjoy it. I may this mistake with my first batch of kids and they don't care to go with me now and it mostly cause they remember how uncomfortable it was.
Your getting lots of good advice. I spend most weekends outdoors with my kids. Pick up other outdoor interest like rock hounding, mushroom hunting, foraging, berry picking, gold paning, tracking, geology and animal watching. This keeps up the interest when hiking and spending time in the woods or where ever your at. I am always like, look at that mushroom and we bust out the book. Or I think you could eat that and look it up. That's a pretty rock etc. Build survival camps, but dont camp that was not a good idea save that for 16 or older.
Oh ya your the mule in this situation. Plan on carrying everthing. Lots of snacks and water. Books maps, rocks, gold pan, extra clothes etc.
The good news is besides finding some wonderful things and places with your kids is that your scouting and discovering cool things and places.
Oh ya go clam digging if you can afford the gas. It's a lot of fun for kids and you get 30 more clams. You can make a kite and make a day our of it on the beach. Or look for cool stuff that washe'd up.