What I don't understand is why the data differs when I change between these lines:
aClass = new AnotherClass(&softSerial); // This will get values on update, but not the right values (pin 2&3).
aClass = new AnotherClass(NULL); // This will get the right values on update (using rx&tx).If I use the first line I wont receive valid data. But if I use the second line everything works great.
So. what about this:
What is not defined is what is connected to what pins, and what the problem is.
You don't say that you are moving whatever is connected to the Rx/TX pins to the software serial pins, so I'll have to assume that you are not. Which explains why you can't read anything from them.