We just use a small flat screen with integrated freeview and DVD (got the Blaupunkt one from Tesco), and just have it on a swing arm bracket to save on space. Does the job fine for us.
All mains powered tv's reduce the mains to 12v inside the set to run the thing. Why not get a cheap mains tv then get your local tv/electronics workshop to by-pass the mains input and provide a 12v socket for use on battery.
I am sure this can be done.
We have said 19" cheapo Alba from Argos that has built in DVD is compact light and runs off 12v all for £99. This is now in our sons end of the caravan. Then we have the cello 22" TV with DVD and satellite receiver £200.
Had to return cello TV (maplin) because there was a white pixel permanently on the screen in the corner but the 2nd one was ok. The Alba has a delay on the remote which you have to get used to. Press button and 2 secs later channel changes.
------------- First van bailey ranger 550/6
Now the proud owner of a coachman amara
I use a 22" Cello 12v non DVD from T* Village in Scotland, excellent picture, sound is a bit tinny in all settings, comes with 12v and 240 mains adaptors
When on 12v i use cigar type socket fitted with 2 pin caravan plug into vans socket
But I use my LG Soundbar 120w, with stacks of sound settings, when on mains hookup, bought from *rgos
Update on my tvs the Alba doesn't support SECAM, but the cello does SECAM being the French system, I thought all tv's were PAL, SECAM,NTSC these days. Finally got round to aligning my maxview dish by bungying it to my awning pole and currently have 808 channels on Astra 2A on the cello traveller. So Alba tv only good for DVDs in France.
------------- First van bailey ranger 550/6
Now the proud owner of a coachman amara