I agree that this is a social, not a mechanical problem, but to reinforce the point, think about this: Sure there are timers that will activate a solenoid to shut off water. That is how your washing machine and dishwasher work. And the pay showers in campgrounds. But it requires electricity and access to the pipes. Of course you only want this timer on the shower, so you must have access to the pipes that supply water to the shower only. If you are lucky, you might have access to this in your basement. Otherwise, you will have to break down a wall by the shower to install the solenoid and provide the electric power. And you need a way to activate the timer. How would you do this? If you've spent thousands to install it in your bathroom, OK, you can place a button there, but otherwise you would have to get your daughter to go down to the basement and press a button to start the hot water before taking her shower. And then you would have to do the same thing when you before you took your shower.
It looks like the mechanical solution is too complicated. Perhaps a conversation with your daughter might make more sense. BTW your water utility might, for free (our does) provide you with a little waterproof timer that you put on your shower wall. Press the button and it will start an egg timer that will beep five minutes later, telling your daughter she should finish up.