On a practical level, I wondered about seeing whether you could arrange to take the dog out for half an hour or so.
Maybe you could buy one of those toys you an put food in, or some treats, and toss that over the fence just before the open house starts, to give the dog something else to do, or arrange for a friend to play with it (if the neighbours are away, how would they know?)
I don't see that making a complaint is wrong , but I would consider whether this is likely to have an effect. Are the council likely to address it quickly enough to have a result by the time the open house is due?
However, if the neighbours are going to be away then one option is simply to mention that, if anyone comments on the dog. "I think he's bored. I believe the neighbours have gone away for the weekend" It's true, and you don't put yourself in the position of lying about it.
Also, if the Open House is only for 30 mins then I would guess it may not be such a major issue as you feel - presumably that would mean that there will be people coming and going - I think mosr people would then assume that the dog barks at people coming and going, not that it barks incessently all day...
Would having music playing in the house help, so the barking wasn't so obvious?
Finally - check with your realtor before you make any complaints - I know in the UK you have to disclose any neighbor disputes to the buyer, when you sell a house, so it would be worth checking whether there are any similar rules where you are.
In your mum's position, I would speak to the husband and ask him about arranging to take the dog out for half hour while the visitors are there. I agree that neighbour was really rude but what you really want if for the open house to go well, so I would do whatever is most likely to achieve that, even if it means letting the neighbor get away with their bad behaviour.
If he won't agree- do you have daughter's phone number? It might be worth calling her just before the open house and asking *her* permission to take the dog out.