I'm not sure what ideas you are looking for. Alternatives to taking him with you? There aren't any, in my opinion. He's yours and you are his, and he is part of your family. Tiles can be repaired or replaced. Floors can be buffed. Etc. If you can afford to move into your "dream home" then you can afford to spiff it up when the day finally comes for him to go to the rainbow bridge.
And definitely talk with your vet. When was the last time he was in for a checkup? Dogs do get dementia with age, and sometimes stubborn or whatever... so do elderly people. Maybe there is a medication that can help with some of it. There may even be something you can give him to ease any stiffness so that the stairs aren't that big of an issue for awhile.
I think if he cannot manage the stairs, then he will let you know, and be content with something of yours to sleep with downstairs, (maybe right near the bottom of the stairs?), as someone else suggested.
My GSD just turned 10. I cannot imagine not taking her with us if we were to move---even into a home that isn't really suited to HER needs. I just can't imagine it. And yes... I know they do "little" things to the house that you don't notice until time goes by. But so do kids. Look around at the door facing in your house... I'd bet they are just as covered with grey hand marks as any other damage the dog might have done over time. Mine are. Just like my dining room window sill gets coated with that greasy "doggy" ick, because she lays with her chin on the window sill all the time. She doesn't do anything wrong, but it still leaves a mess. So I get it. But I would still take her with me. She's my girl. And we are the only family she has.
She would die of heartbreak and depression pretty quickly, I'd venture to guess, if we tried to find her another family to live with. That's awful to contemplate if it isn't truly a necessity (a single owner who passes away and leaves behind their companion pet type scenario).
It isn't a necessity to not take your dog. So take him. Your kids need to learn how to navigate around him (and dogs in general anyway). No food at his mouth level. It's that simple. Kids should be at the table with food anyway.. not walking around with it. And sure, he might accidentally knock your little one over sometimes, but she is growing quickly, and she WILL learn to watch out for that. Kids are amazing at what they learn in the name of self-preservation and natural cause and effect.
I suspect that some of his "obedience training" that didn't work, is simply a matter of you have gotten busier and more distracted with the children and your own lives and haven't put into enforcing the rules what you should have of late. Step up your game a little bit there, and you will see a difference. But, that means not just disciplining the dog and being a rule keeper for him, but for the kiddos as well (remember--food at the table, not walking around with it).
You'll be glad you put in all the work later on...because when the time finally does come... in a year, or three or 3 months from now... and you have to make that final vet visit, he will be your big baby all over again. And you will be in pieces. Don't rush going there. Let your kids have him for as long as they can. He is a part of the family for them more than for you, even... they don't know family without him, do they?
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Oh.. and that is a good point, that once you move EVERYTHING will be new all over again. It will be a great time to (re)introduce rules and practices. I know that our GSD is accustomed to certain behaviors of mine (like staying up late at night). While she naps nearby... she also knows that I will take her out one more time before I retire for the night.. usually around 1:00 a.m. So, when I am trying to go to bed early for some reason, she doesn't quite "get" that THIS is her last chance at the potty for the night. So by morning, she is READY at 6:00 a.m, when normally, she doesn't seem in any rush to go out until after 9:00 a.m. sometimes.
It takes time for new routines to become the routine. So be mindful of that when you move. From the first day/night in the new place, be very proactive in your behaviors and expectations with him. So that he will learn the rules of the new place. And that includes night time potty breaks, and possibly taking up his water at bedtime (or reducing how much is available to him throughout the night). But certainly, please ask his vet about medical reasons behind his night time interests/needs, and possible medication to help with it.
I do get that he is very large. My former boss had a great dane.. so I understand the size thing. But they also tend to not move all that quickly--well, I never saw Rocky move fast at all. I don't know about your fellow, but at 11, maybe 12, he is probably only the slower side, no? So it doesn't seem likely that he is running your toddler over... more like turning around and not seeing her as she stands there and gets bumped over, right? The biggest concern with that, would of course be the stairs. Don't allow the dog up the stairs and that is fixed. New house, new rules.
I hope you get some sleep though. Any chance of going back to using his crate when you make the move? That might help with the nighttime issues, too.