Agree with the opinions above, I have a dog and young children too, I have had to train them to be very careful, and always to check the cats are shut in safely before opening the front door.
You can screen windows with trellis cut to size and velcroed in place, or beading covered with fine mesh.
there are companies that will cat proof your garden for you, or some people have done it themselves with hanging basket brackets attached to their fence panels, leaning in, with net over the top.
Cat Fence: Purrfect Cat Enclosures and Cat Fences
Katzecure – cat fencing for cat breeders and cat owners alike