Hello Crane,
Welcome to the forums, I am sure that you will enjoy your time here, now about your Mobile Home. If you intend to leave it here full time then you have to, by law, re-register it onto Spanish plates. You may use the MH on the UK plates for a period of six (6) months only (tourist), no you cannot take it to France for the day and return it to the land that it came from.
If you intend to leave it here in Spain for 12 (twelve) months then you will have to make a SORN statement back in the UK and then re-register it here in Spain, as its an old lady there is no import tax to pay on it. You might find that you will have to ITV (MOT) it twice a year here if you intend to use it on the road system. If however you decide to keep it on UK plates then you must return to the UK to Tax, Insure, and MOT it each six (6) to twelve (12) months.
If you are not going to use it on the road system, then consider removing the wheels and place on jack's or axel stands, so that your friendly Police can see that its not going to be moved.
I do hope this helps you.
David SR.