Taking pictures of my dogs without permission

Very legal. You can ask, since they're your dogs, but the photos belong to the people who took them, so it's really up to the copyright owners of those photos to decide if you should get one for free or not.

Your dogs were in public so you had every expectation they'd be looked at and photographed, your dogs have no publicity or privacy rights to their images (or any existential awareness of their images, for that matter), and you have no such rights in your dogs' images.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.

Oh my. I assume you see your dogs every day. If you want a photograph of your dogs then take one.

But if you want a photograph of your dogs taken by someone else then buy it. The fact that your dogs are in the photograph has no legal, moral, ethical, or any reasonable bearing on whether you have to buy that photograph or not.

I agree with my colleagues - perfectly legal. You could ask if the person will give you a picture since they are your dogs, but they are not required to do so.

The answer might be different if your dog was already famous, but that doesn't sound like the case.