"They have to find a new car."
Translation:De måste hitta en ny bil.
And what is 'not have to'? I have heard you cannot say "De måste inte" but instead "de är inte tvungna"? Is that right?
have to is more måste. For blev tvungna, I would say were forced to in English. There is also a difference in time here. have to is present, so if you were to use tvungen it would be är tvungna instead. It's still a bit stronger than have to and closer to are forced to.