I have a PS4 at my dad’s house and at my mum’s house. Can I play FIFA at both houses or do I need to have two different FIFAs?

Yes, you can play all your games at both houses. There are different things to keep in mind, depending on whether you own a physical copy of the game (a disk) or a digital one.

Physical copy

Simply carry the disk with you and put it in the PS4 you want to play with. You'll need to remember to bring the game with you, but you won't need an account for that.

Using the same account on both consoles is still recommended for various reasons (see below).

Digital copy

On both PS4s, you will need to log in to the same account on which you bought the game. You will also need to download the game to both PS4s.

Both

To play online, you will need an active PS Plus subscription on both consoles. If the subscription is tied to your account, you only need one such subscription. If both your parents have their own subscription tied to their own account, you won't need a subscription as long as you're playing on their PS4 system.

Besides that, you'll probably want to keep the same progress on both consoles. For that, you will need to log in to the same account on both consoles. You can either copy the save game to a USB key and carry it along with you, or you can use the Cloud Save feature provided by PS Plus. While the PS4 can automatically sync save games with the cloud, for some reason it only does so once a day (in my case it happens sometime between 3 and 5 AM). Depending on when the automatic sync happens and when you move between houses, you might want to remember uploading the save games manually before leaving, and downloading them manually before playing the game.