I high school and amateur rodeoed for about 6 years, from age 14-19. I team roped (heeled for high school rodeos and was a switch-ender for jackpots and amateur shows) and calf roped and did a bit of bull doggin'. My dad and his siblings as well as his dad were all rodeo cowboys for many years, and were very successful. Little claim to fame, but my uncle competed in high school and college against Cody Ohl (the proverbial villain of Pro Rodeo) and spent several years kicking his butt until mental illness took him from us way too young. Rodeo was all just part of growing up and I wouldn't trade those days for hardly anything. Calf Roping took its tole on my knees, and at the ripe old age of 28 I've had 2 reconstructive surgeries on my left one and both of them ache anytime it gets cold. I'm screwed once I get old...
The funnest part was all the time spent in the truck with my family (about 115k miles in 4 years of high school rodeo, for example). I never had any time to get into trouble because dad was always there, driving the long hours and helping warm up horses and push calves and steers. He and I competed together as well in team roping jackpots and local rodeos and were quite successful in doing so. In my opinion, rodeo is the ultimate family sport. Most parents in their right mind wouldn't turn a 17 year old loose with a $75k pickup and a $100k trailer and $50k in horses, so inevitably it becomes a family affair.
Additionally, where it sounds like you've never done it before, be warned that the costs will add up. If they do timed events, good horses are as expensive as they've ever been. People will tell you to just get a dead broke horse and teach it yourself, but if you want your kids to have a snowball's chance of success, that horse needs to be automatic and unfazed by their cluelessness. When I was starting, my dad ended up driving to another state to pick up the heeling horse that I rode for many years, sheerly because she was legitimately automatic. I've got videos from later in my career where I roped steers with nothing but a twine string around her neck as a means to neck rein her, she was that good. And that's the reason I was successful, was because we found a horse that was automatic that allowed me to just work on me while I was still clueless. A good, broke rope horse will start you between 10 and 15k pretty easy, and that's just the horse. Then, there's the tack. Add another couple grand and you'll be there. Then there's the feed. Then little things, like ropes. I usually went through 2 ropes a week, and they're about $50 each. Like I said, it ain't cheap.
If they're doing rough stock, then you don't have the horse investments, but you're gonna wanna pay for all the best safety equipment as well as as many schools as you can get them in. Rough stock is dangerous when you know what you're doing, it's deadly if you don't. A good bareback riding school with a guy like Kaycee Feild will require a small loan to invest in for them, or a saddle bronc school with Billy Etbauer will be the same.
Feel free to send me a PM. Rodeo is in my blood, and although I haven't competed in about 9 years, we've lived it long enough that I feel like I could give a good idea of what you can expect and how to navigate the politics of it all.