When spraying pesticides it is recommended that animals and humans stay off the lawn until the liquid application is dry to limit exposure. As the liquid dries the amount of chemical that gets on you decreases. Try to keep pets and children away from the area for about 4 hours for the area to dry.
Many people have problems with dogs, in particular, "going"; on the lawn and killing the lawn. Female dogs tend to be the bigger culprits because they tend to squat and pee in one place, where males will mark their territory in many places. Urine is high in nitrogen, but instead on giving the grass some fertilizer it actually burns the grass. The brown spot that results will often have a green ring around the outside. The nitrogen overload at the center causes the grass to burn, but as the urine is diluted toward the edge, it has a fertilizer effect. Faeces on the other had decompose slowly, which gives the owner a chance to remove it or it breaks down slowly fertilizing the garden organically.
Try to walk your dog as much as possible to ensure that they are not going on your lawn. Also train the pet to go to the toilet designated area of the yard. You can landscape the area specifically designed for the dog. It will need a substrate like gravel or mulch that the dog finds acceptable and may even include a marking post like a large boulder, bird bath, lawn ornament, or even faux hydrant. Use hormone bought from a pet store to give them the scent and move all faeces into this area. Initially, training can occur with the dog on a short leash and food rewards employed to encourage use of this area. Many dog owners will also find it helpful to train their dog to toilet on command during this time. Common commands might include: Toilet or Potty, etc.
Dogs love digging, if you have a dog that digs up your garden it is usually because it is bored. Give them some toys to play with, rotating the toys every few weeks so they become new again. If this doesn't help consider a digging pit, this could be a children’s sand box or a hole filled with sand marked out by pine logs. Bury treats and toys under the sand for when you are away and train you dog to dig with the command “dig” and rewarded with a treat to encourage them to dig there and not in your garden.