Here are some options for the dog wash station:
You could do a bar like this with a couple rings attached
Or two small handles mounted wherever you need:
Or simple rings mounted where every you need:
Here is a link to the mini-split AC/heating system I suggested. They’re affordable and they work great for a small room. If I were a general contractor, I could install this for you, but unfortunately you’ll have to go with an HVAC company or general contractor.