Hello Geordie Girl,
I get the impression most of the other replies are suggesting you should get a leisure battery. I'm not so sure you need to, In fact I think a relatively cheap small car starter battery mightbe better for your stated needs.
Let me explain.
As you tell us, you only need the battery for the motor mover, then we only need to consider the energy the mover needs, and it's not as much as many people may think!
The specification for caravan movers will tell you what the full load current requirements of the mover are, and most will be about 40Amps. It is the nature of electric motors to have a big inrush starting current to get the motor to initially turn, but as soon as there is some movement the motor will start to generate a back EMF which opposes the supply current and the current demands falls. We are talking of a fraction of a second for this to happen. So the starting current is high, but the running current is usually quite a lot lower. It does depend on what, and where it's moving it, but on a flat surface a running current might only be from 40 down to 15A in under a quarter of a second. In terms of the power actually used broadly speaking we can ignore the startup current usage as it is so short lived.
However there are some movers which have a "soft start" system which is supposed to slowly ramp up the motor speed, but that does not always mean the peak currents are reduced, IN fact if it's "chopping" the current, that can create a series of startup peak currents, which may be more significant in terms of demands on a battery it all depends on how the control manages the process.
So you need a battery that can deliver the motor starting current. Small Gel type batteries may not like the starting current which could actually a damage them, where as a car starter battery is designed to have a very high engine cranking current which would be no problem for a caravan mover.
That covers the peak currents but we also need to look at the total power a caravan mover uses. Fairly obviously the longer a caravan mover is used the more power it will consume. but think carefully about how long the motors are actually running, Unless you have a very long way to move the caravan, most activations only last perhaps a minute. So you need to hitch up at home, unhitch at sight, re hitch at site and unhitch at home. That four activations, for some people that might only a total of 4 mins! but let's be cruel and say each time was 5 mins, that a total of 20Min or 1/3 of an hour. Ignoring the start up peaks and assuming they would easily be absorbed into the 5 min run times that's 15A x 1/3 hour = 5Amp Hour
To put that into context that like running a Truma blown air fan at fairly high speed or a classic caravan fluorescent lamp continuously for 4 to 5 hours!
With such a small total power demand, even the smallest fully charged car battery would cope with that quite happily, even if the currents were twice as big it would still withstand being left partially discharged for the duration of the holiday without damage.
For you application I'd go with a cheap and cheerful small car battery,and just make sure it's properly charged when you get home.