My Bam had a terrible poopy-butt for a long time and I had to read up on the subject. Hay hay and more hay is what’s recommended if there’s sth wrong with the bacterial flora in the intestines – sth that can happen pretty easily to a bunny, but can take a good long time (3-6 months) to resolve. With Bam, I caused the problem by feeding him a bunny-müesli with all kinds of delicious but bunny-inappropriate stuff in it. He loved it, but it ruined his stomach.
I cut him off from pellets, treats, carrots and fruit. Some veggies he could tolerate a little bit of, like mint and dandelion greens, but dried greens (dandelion, oregano, mint, lemon balm, tarragon, kale) worked better. I also gave him apple-twigs and twigs of willow (the bark has a slightly astrigent effect) + I dried lots of apple-peel. I still had to give him butt-baths several times a week and cut the fur around his butt with scissors and put a home-made barrier cream on him to protect the skin. But then slowly it started to resolve and he became better, slowly but steadily.
I consider him cured now, but I still never give him carrot. He can have dried apple though. He also gets pellets and fresh greens now, but I still take care that he eats his hay by serving it in smaller wads over the day – for some reason, freshly served hay is more appetizing than hay thats been available all day. I also have an all-grass pellet, organic, that he’s learned to like.
I understand that you’re in a stressful situation. This is in most cases a resolvable issue though. It’s not caused by a disease, it’s about the intestines having been colonized by the wrong bacteria.
Here’s a quotation from an excellent article on rabbits’ gastro-intestinal physiology http://www.medirabbit.com/EN/GI_diseases/Rees-Davies.pdf
Most of the common gastro-
intestinal problems seen in captive rabbits are related to inappropriate
diets (low fiber; high protein; high carbohydrate) and infrequent feeding
of treats to which the rabbit is not accustomed. Many of these problems can
be avoided if captive rabbits are fed a diet consisting primarily of fibrous
vegetation, such as grass, hay, and fibrous weeds. Feeding of fruits, grains,
and carbohydrate or fat-based treats should be avoided. Pelleted feeds,
although convenient, should be kept to a minimum, and where pellets used
those manufactured by an extrusion process, which retains the long particle-length of the indigestible fiber, should be chosen.