The OP doesn't say she is afraid of a dog lying on a rug asleep but unless you are very experienced with animal behaviour then you have no idea if a dog can wake up and become aggressive if a child cries (even if just at the sight of a stranger).
And one of the dogs that the family refused to put away was clearly aggressive.
Most of the dog owners on this thread are living in a world where dog owners are responsible and sensitive to visitors, the general public is not afraid of dogs and also the general public is good at reading dog behaviour.
The OP is living in a world where she has no idea if a dog owner is responsible, where families are clearly not sensitive to visitors, and where she is not an expert in dog behaviour but is mildly afraid of dogs (both through personal experience and through colleagues' misfortune).
I would report the families that refused to put their dogs away and say you won't visit them again unless they put the dog away.
I am assuming you make an appointment? though in some jobs you would just turn up in the home.
So maybe if you could ask every family when you ring if they have a dog, state that there have been cases of dog bites and that you will require dogs to be shut away. If they say "oh but he's a softie" then say "sorry that's policy now" [never mind it's your own personal policy].
Then you can book for a colleague to go and you swap to his/her family if someone is reluctant. Should save you wasted visits as you can swap and go to a non-dog household if a colleague is happy to take your place.
If you ARE involved in safeguarding, this is a safeguarding issue. Children of the family or visiting children could also be afraid of the dog.