Thanks for your question. A dog is always a difficult issue because emotions are involved. The law is, however, that a dog is deemed to be property and not a person. If the dog wasn't dealt with in the division of property in the divorce then the legal position is that the dog is still joint property.
You could raise court action so as to get an order to declare the dog as joint property and to have shared possession. Most judges would tell you to go and sort it out yourselves, however, so perhaps the threat of court action would suffice to you here. Happy to discuss further.
It really doesn't matter whether you paid or not.
The issue is their intention at the time that the products were taken.
I'm so sorry. That answer was meant for another post.
I did not mean to respond to this and will opt out.