I think it is really a bit silly to have reached the years of discretion and claim to be afraid of dogs.
What do you do out in the park with your grandchildren? If you fuss and flap you are going to encourage them in an irrational fear (and are more likely to encourage the dogs to become over-excited)
And dogs, like people are not all the same. Yes some might be dangerous (guard dogs for instance) some are soppy , some are shy and retiring themselves but it is important to remain calm
Anybody owning a dog would have, I hope, the manners to shut it away when visitors call, but really, to let such a silly thing come between your DH and his mother on Mother’s Day is IMO nothing short of selfish of you, especially if she is really elderly.