Yes, there are veterinarians in Manta and Salinas. In Libertad (near Salinas) I’ve heard recommendations for a vet office called El Pibe. Dr. Franklin, there, and his wife Maria both speak English and they are there most days and available by phone at other times: 097000803. I understand they board large dogs at El Pibe — at the vet office and in a separate area than ill animals but still mostly indoors. Smaller dogs are boarded at Dr. Franklin’s home.
I don’t have a contact for you in Manta, unfortunately, but it is about 6 times larger than Salinas and I’m sure you will find services there. Once you put down roots I’m sure you’ll find what you need. I have a house-sitter who stays in my home with my cats for $10 a day. She charges more for dog sitting – -not sure but it may be $15 a day. This is just to give you an idea of what you might expect to pay…