I suspect the problem will be a bit more logistical and practical:
1. The program rules say that the points need to accrue to the person paying the bill, so in that case you'd need to ensure your kids have cash or some form of debit/credit card to pay.
2. A lot of hotels won't let someone under a certain age check-in, at least not alone, likely set by their local jurisdiction (21 or 18), and their desire to avoid teenage parties/problems
You can probably overcome some of these with a guarantee letter, but that is a logistical hurdle.

I guess I'd be interested to see the outcome and plan, I had considered doing this recently even for my wife for our second room (as we typically need one due to kids), but then I realised I'd be sacrificing the 75% bonus points for being Titanium, and adding complexity around check-in/out. In our case for 40% of our stays (let's say 30 nights/year) we could do that, you benefit from bonuses and if you travel alone, but lose the bonus points to the main account. I see airmiles as a bit different as I do buy a seat for the kid, and am allowed an account for them as a result, most of the time in the hotel its a bit like an in-seat infant, they're sharing the bedroom!

Just one final thought: Are you sure you want to introduce your kids to Marriott so early... Pre-Marriott (I blame work as a consultant) I used to choose based on price/quality/location, now I just choose the most suitable Marriott in a town, even if its the only one, and I'm sure I pay a premium for an intangible potential upgrade - it doesn't matter now, but 18-year old me probably needed the $10 difference for beer money (in Europe)...