I agree that it's unreasonable to expect other people to see your dog as the same as a child. Perfectly fine to celebrate mother's day as a dog mother, if it floats your boat. Unreasonable to expect others to acknowledge it if they don't see it that way because that's the point it has an impact on other people.
But people believing their children are dogs only really seems to be a problem because it irritates you a bit. It's not an actual problem.
My DH has a real issue with dogs wearing clothing, because clothing is for humans. I think if it makes their owners happy, then good for them. Life can be really hard and miserable sometimes - if putting a jumper on your dog or throwing yourself a (slightly odd) mother's day party keeps you going, then have at it. This all means that dogs wearing clothes is a problem which is wholly owned by DH. Not a problem for the owner, not for the dog, not for me, not for society - because it doesn't harm anyone else.
Some people can't have children, but they still have maternal feelings. Does this mean they shouldn't be allowed to have those feelings because only a child should be deemed highly enough to deserve them? Who gets to decide that?
As a society, we step in, judge, and prosecute people at the point of their actions have a harmful effect on other people. So I think the position of - fine for you to feel that way as long as you don't expect other people to take action to accommodate it - is a reasonable one.
We don't get to judge other people's feelings as valid or invalid. That's unique to each individual. We judge harmful actions (or thoughts, if you include prejudice).