Not sure if this has been experienced by anyone else (I'd never seen it happen prior to 1.8), but I adopted Sofie, and another time I adopted Francois (boy, that kid must get a lot of wedgies with that name...) and Sissel from the orphanage, and both times, I'm greeted with "A DOGGY? I DIDN'T KNOW YOU HAD A DOGGIE MAMMA! CAN I KEEP HIM/HER? PUH-WEEESE?" the first time that I left and came back (meaning after having already met them at a house from the orphanage or wherever), both to Sofie and to Francois and Sissel. Yet I have no freaking dog! Worse yet, I can't even get a dog to partner up with me, since I apparently already have an animal companion. Argghhghg.

What is causing this? No matter what you say to the kid or kids, whether it's "sure, take care of him when I'm gone..." or "no, you brats can't even take care of a pet rock." (I can't quite remember what the choices are...that was probably obvious though...ahem...), I gather you're delaying their kinda cute/somewhat annoying "look mommy! I found a...."/first pet episode for like 2 or 3 in-game years. Their AI or whatever is either going to think that they have a pet if you say yes, or if you say no, they'll either never ask again or do all of the annoying things like 3-4,000x first before bringing home a rat or that other gross thing...and I don't know about you, but I'm NOT real keen on coming home at 3 AM, after saving a town from crazed vampires and a dragon, among other things, just to repeatedly learn how

A.) my steward is the worst. Babysitter. Ever.
and thanks to that fact, I get to
B.) find out that my child is not only dumb enough to not immediately jump in bed and act like she's asleep when I come home, but actually asks my ragged, worn out, sleep-deprived and, let's face it, severely wounded ass (who knows how much blood the Dragonborn would need after a bender?) if I wanna play a game at 3:00 AM!

Wait...ranting about this just jarred my memory--now I remember how I fixed it the first time! Hey, this might be helpful!

Usually when I get home after "an adventure" or whatever, I save it before entering (in case something awful awaits viz. my children's bugginess...), and so after both of my kids hallucinated my dog (the first time was a few days ago, when I had a trial adoption with Francois and Sissel), I reloaded my save just before I entered the front door, went looking for Meeko, told him to tag along, then told him to go home. I quick traveled home (and you are DAMN RIGHT THAT I saved THE GAME again before I went in the door!), and instead of making up nonsensical animals, they were arguing, like healthy, normal kids! Whew...(if only you could send them to their rooms...).

Too bad I had to marry that HUCKSTER/TRAMP, ANWEN! I was so heartbroken that I had to reload my save from before I adopted those two rascals...(though I guess that I did keep the one I made just before I adopted them...)

Also: when it happened, I had been at Fort Dawnguard, near the dogs. I went back to make sure that they hadn't done that thing where they fall through the floor or whatever, and trying to get them as followers (I had Kharjo with me too) is what made me realize that it was bugginess.

Well, if I didn't help anyone, at least I helped myself : )

The invisible dog you never knew you had is an ancient glitch, would not surprise me if it has been there since the game was released. Glad to see you remembered how to get rid of the dog.