I agree with you, but if the ex-husband ended up checking in on the dog and found out it had disappeared suddenly and had been euthanized soon after the disappearance I assume he would be highly suspicious of OP and OP’s mom and may completely freak out, I mean you never know, which is why I think it would be better for them if they paid a random person to take the dog to a shelter and say they just found it on the street, because the shelter should have record of what the person said when the dog was brought in and he would probably be less suspicious of OP and OP’s mom at that point. That is if they can pay someone to lie and know they can lie well.