OK, some suggestions:
As it's a big garden get some old carpet squares, & pop these down. The slugs will crawl under them during daylight hours for protection. In the morning, turn them over and provide breakfast for the birds.
Have a bit of an untidy log pile somewhere (with plenty of gaps) and hopefully you'll have a frog or two or hedgehog move in and eat the blighters
Beer traps, with a couple of sticks planted nearby to stop the dogs having a party (have dogs myself). Even better, put the traps under the plants affected (making sure the slugs can't use the plants to climb back out)
Use sand/grit/gravel to deter the slugs and snails from getting to your plants
Use copper tape around any planters to stop them. You might need a double strip of tape (two sets of tape about an inch apart) to stop the really big ones. This also works on PVC / polycarbonate greenhouses & cloches.
Grapefruit halves - eat the grapefruit & put the empty halves down to form domes. this works the same as the carpet, the slugs crawl underneath, and you turn them back over to let the birds have breakfast.
I'd also net your veg patch, I have NO lettuces left after the sparrows have pulled them to bits. I will be using this when I finally move later on (we have a house over the road that was my father-in-laws, where the garden is MUCH bigger), I have a couple of cheap hanging baskets covered in net, upside-down over my salad patch now, to make sure I get some lettuce and not just the birds.
The growing success pellets are safe for kids and dogs, but I don't need to use these any more, since I have had 2 frogs move in, I seem to have a lot less slugs than last year, and the rest I keep at bay using sharp sand.
You can keep birds away from your veggies using shiny things like wind spinners, or get the kids involved by making a shiny scarecrow, by stringing up strips of tinfoil & old tart/cake cases suspended on a string across the top of your veggie plot, apparently birds don't like shiny things (apart from magpies). I'd still encourage the birds, by putting feeders in a separate area of the garden, as you want them to help by eating the insects in the garden, and if they know they can go to your garden for a 2 course meal (slugs followed by some seed or peanuts), they will help.
Hope this gives you some ideas, as I also have 2 little ones and a hoofing great big dog (but small garden)!