Any suggestions, or is this something everyone goes through & I just have to slog?
It's definitely something everyone goes through. However, there are some strategies to ease this process, and I'm sure your teacher can assist. What I usually do is:
1) Learn both hands separately at a very slow tempo.
2) Combine both hands at this very slow tempo.
3) Then separate hands again.
4) Return to 1 with "slow tempo" instead of "very slow tempo".
Having played both hands together at a very slow tempo then makes your life a lot easier when putting them together at a proper tempo again. There are certain pieces that support the process of coordinating your hands. Pieces from Bach's "Notenbüchlein für Anna Magdalena Bach", for example, are excellent and so are the first ones from Schumann's "Album für die Jugend". Since you've just started, Bach's 2-part inventions are out of your reach, but these are too brilliant pieces that will definitely improve your coordination skills once you've reached a certain level.
It takes time, but it's worth it!