Other Long-bodied dogs?

Apart from Dachshunds?

And what problems could arise when restraining a long bodied dog?

bassett hounds
What do you mean by restraining? Actually, all long bodied dogs enjoy the same issues (bassets, corgi's etc)

Do you mean using a leash? There's no problem walking a long bodied dog on leash.

Back issues arise, when you allow these low-long bodied breeds to catch fat and out of shape.
Answers:    BASSETT HOUND
CORGI
SCOTTISH TERRIER
SKYE TERRIER
SHIH TZU

Keep them at a fit weight and don't let them jump--the biggest problem is put a bet on problems which can often be avoided by this.

Other long bodied like Corgi? Not certain what you mean by restrained.
basset hounds, corgis, dandie dinmonts, bichons the list go on...

and what exactly do you mean by restraining?
Does anyone nurture their dog Solid Gold?   What do you expect of the mark of my Grandma's dog?   Can a muzzle be not here on a dog 24/7?   Why does he catch these lump things?