I've e-mailed a friend who is a trainer and expert on dog behaviour, and has several dogs herself to whom she is totally dedicated- to see if perhaps my response was too cautious. And here is her reply:
I am of the opinion that one must never put a dog in a position that he might not be able to handle. It simply isn't fair - not to the child, not to the adults, and certainly not to the dog. Because the dog will pay the price if, doG forbid, an adult takes his eyes off the ball.
It can be even more difficult with multiple dogs who do not normally live together, as the pack dynamics will take some adjusting. Even dogs who are normally good with children might be upset by the advent of outsider dogs into their territory. Tensions might rise in the ensuing adjustment period, and displacement can be a possibility.
I have also found that sometimes guest dog owners who themselves do not have problems with their own dogs have difficulty understanding that other dogs might not react as theirs do, and so do not understand the need for caution - making the situation even more fraught.
If the home can be managed with an iron-clad rule of adult supervision at all times of the dogs with each other as well as of the dogs with the baby with an absolute 'child-free' or 'dog-free' division of the area, then perhaps it will be fine. But if that sounds like less like a holiday and more like a prison... perhaps it would be best if holiday care for the dogs was found for the time the child is visiting.
I know that I would not put my own dogs in such a situation. And I certainly would not want to spend a holiday with that level of stress.