I have been on the site for 4 years and I think I can remember 1 story (JRUSS) where there was zero hint of OM. My ex coincidentally dated a guy she use to work with after our D. Shocker huh? Quite frankly since you are so determined on recon I think you are better off there is an OM. If not, that would have meant she gave up everything because she didn't like you very much.
Of course she is going to lie and not tell you that OM made it for her. That's another reason for no small talk, stay out of the house when possible and stick to strictly business.
Look, I never had pets so I am not sure I should comment but if you don't want the dog don't keep it. It will be tough to tell, your kids but they will get over it. I would definitely let your W know to not ever put you on the spot like that again.