The sims 4 install on two PC's?

When you say she cant play it at the same time does that mean the game she started at her dads must stay at her dads unless the details are transferred to my computer?
She can't play it at the same time, as in, she can't start the game at her moms house and also at her dad house, one of the games will give an error when that would happen. 

If she starts a new world here she would in essence have two different worlds to play with at her different homes - but the two wouldn't interfere with each other?

Indeed. She can play 2 different games with different save files. 
Or she can make a back up and take the back up with her to the home she is going to. 
Depends on what she prefers, two different games or one and the same game. 

So you know, you can install the game on both devices with the same Origin account you first installed with. For the first computer you need to give the serial. For the second computer, you can find the game in 'my games' and install it through there.