Hi Karen,
The dislike of closeness suggests Liver Qi stagnation, which in itself is a Liver 'weakness', in the sense that the Liver is the organ of confidence and 'putting oneself out there in the world'. If the Liver (or Wood) is weak in that sense, then Metal is strong, which in excess is the element of controlling variables, disliking change, building walls, and hiding away.
Other elements that support this picture:
- eye redness, common in Liver Qi stagnation and secondary Stasis Heat;
- restlessness at night; when Liver Qi is most internalized
- secondary Stomach Fire, which can occur with Stasis Heat or even primary Liver Yin deficiency, and causes an excess appetite
Liver Blood and Yin deficiency is the main cause of this picture in dogs. Given the appetite, I'd suggest Liver Yin deficiency.
The formula to consider is Yi Guan Jian. It will work slowly over a few months IF the owners also get the dog onto an unprocessed meat and vegetable diet.
There are other considerations - Xiao Yao San, for example - but I'd go with YGJ first, given everything you've mentioned
Hope it helps,
Steve