Neurologists generally don't throw around MS diagnoses willy-nilly, so I'm assuming you were both diagnosed on objective evidence. If you feel there were any inconsistencies or question marks in either of your diagnoses, I can only recommend getting a second opinion, but the operative words are "inconsistencies or question marks". If you have MS, you have it and finding the doctor who says you don't isn't anything but harmful, even if it's what you wish were true.
I'd just recommend keeping your kids in the loop. Kids are perceptive and will fill any information vacuum with things that are usually far worse than the truth of the matter. You and your wife can best help them by adhering to your DMDs, being open and honest, and as they grow older having them help out around the house in age-appropriate ways.
The prognosis for MS is unpredictable, but it is NOT a death sentence or even a guarantee of profound disability. The unknown can be maddening, but you and your wife at the very least have an intimate understanding of each others' challenges. Look, it's not fair but sometimes health lightning does strike twice. Both of my parents died when I was a kid, both from unrelated, non-behaviour or environment-related cancers. It happens, it *****, but life goes on.
Could it be something else? Anything is possible... Although if you have been having regular MRI's and seeing a neurologist you would hope that they would have picked up on it if it was something else being that your wife is going on 10 years and you 5 years.
As for your children I believe the statistics are that if one of your parents has MS then the child has a 3% chance, what the odds are if both parents have it... I don't know but it's not genetic so there is a lot of hope for your kids.
No one knows yet what causes it it's just us lucky ones that get to live with it with no answers :( the infamous 'they' say that it could be environmental due to higher numbers in certain places etc..
Good luck in your search for answers,
Jane