I have three Burmese cats, who are daft as brushes, we did have five, one had to be put to sleep and another disappeared. The old one use to run up and down the back of the sofa when my daughter cried, I use to let her cry for a few minutes when she woke up, but he got very concerned I wasn't taking any noticeof her and used to pull my shirt, to attract my attention!
I have never had a problem with my cats, I have looked after about 30 children over the past 13 years and without exception none have been scratched or hurt by the cats. The cats are very good at learning to keep out of a crawling babies way!
In fact one of the mums of the babies I looked after was allergic to cats, over a period of several month she became desensitised to them. Whe she first use to visit, she would be reaching for her inhaler in five minutes and sneezing and nose streaming. One year later, nothing at all.
The only problem is my own daughter, she has had asttma from the age of 2, now 15, and has become allergic to one of the cats. She wouldn't possibly entertai the idea of him going to my parents. We just make sure he stays out of her bedroom.
I find most people are very keen for their children to have contact with animals. especially if they have none of their own. We also had a guide dog puppy for a year, and I had a baby too, It was no problem, I kept the puppy in the playpen!