Routine constipation in dogs can be treated through a change in diet (e.g. by adding bran). But clearly (if your canine pal is already on a specific diet) that's inappropriate here. You need to go back to your vet and mention the need for a 'stool softener' (which your vet can easily provide), to make 'going to the loo' far easier for Fido.
Because we only feed raw meat and bones etc. to our dogs they will sometimes get a bit blocked up if we feed to much bone, this is always sorted within a few hours of feeding some extra liver, also if we feed too much liver it will give them the sh!ts.
you really don't need to be around 3 Wolfhounds with the sh!ts I can tell you.!!!
She is obviously on a prescription diet for a reason, and no one should be advising of any additions to her diet if they dont know the medical reason for it. I would speak to your vet first. Definitely no raw liver.