In theory, yes.
But you may want to consider alternative options, since you run into the possibility of the occasionally-unpredictable MDE system not liking it if you both happen to try using it at the same time.
First off, regardless of the Mobile Ordering situation, I always suggest that every adult on a trip have their own My Disney Experience account. Then inter-connect everyone on the trip as friends. This gives the most flexibility when a group splits up. It also minimizes the potential issues on future trips that aren't with you, making sure that things like MagicBands they may have on their account are good on the future trips. (Because the Bands will be "owned" by each person rather than the master account holder who controls multiple "managed by them" profiles)
Second, when you check in and set up room charging, you can have them link everyone's room charge account to your credit card. That will cover any in-person ordering and shopping.
However, since mobile ordering apparently still doesn't allow for room charging, your alternative to having your kids use your MDE account is to have each of them log into their own MDE account before the trip and then save *your* credit card info as the Payment Method on their account. That's what the MDE app will use when they use Mobile Ordering, however the order itself will be made through their MDE account login, not yours.
Hope that helps.
-Rob