Gordon,
You have my sympathy.
I am in a very similar position to you, in as much as I half own an aeroplane with a very good friend. It has worked very well for us. Plane always avaliable when we need it and we also fly a lot together, so we are never short of constructive criticsm from the right hand seat. We have also pushed each other to do Night, IMC and Multi.
Luckily we are still good friends and its working very well. We too have no 'contract' and with only two in the group who has the deciding vote?
IMHO it is very black and white. Your friend is completely changing the basis on which you bought and currently operate the aeroplane. Even though you don't have a contract, you do have 'an understanding'. He is the one 'in the wrong'.
He cannot change the base of the aeroplane without your consent. If he wants these two week blocks, then that's fine, but HE must incur the cost and time of positioning and repositioning the plane to his local field, all within his two week window.
He will soon get fed up, especially if he suddenly needs the plane to go somewhere during your two weeks. As someone said, never trust a bloke who follows his d**k. Once the girlfriend finds out how unreasonable he his, she'll soon drop him, plane or not. I bet he's got a very big watch.
But, could you perhaps post a picture of the plane and the girlfriend so that we can all decide....
Good Luck
3Y