As long as the Onslaught treated area has had time to dry, it's safe for the dogs to chew rawhide on the carpet.
You should vacuum before applying Onslaught and then wait 24 hours after application to do so again.
Without knowing exactly what you are treating for, it is hard for us to make a product recommendation that will fit your specific needs. We do carry a product called Onslaught and it is widely used for general pest control and is labeled for over 200 different insects. You will mix and apply according to the product label instructions when the children and dogs are not in the area. Once it is dried completely, they can re-enter the treated areas. Please read the product label for mixing and application instructions. Please click on the link below for the contact information to your local cooperative extension office for a pest identification.
http://www.csrees.usda.gov/Extension/
Onslaught will kill mites in general, but the problem with mites is finding the breeding source. Onslaught may provide some relief, however many times mites will breed under carpet or in wall voids, where you cannot spray. This is why treating for mites is very difficult and usually requires multiple products and lots of vacuuming.
You can apply monthly on the exterior of the structure for control but the nesting sites that are near the structure should be removed to fully eliminate them. The source of the infestation is very important and is the key to getting rid of the mites for good. Thoroughly apply as a fine particle broadcast spray using a hand pump sprayer to infested rugs and carpets and other cracks and crevices around the perimeter of each room. Put all clothes through the dryer on high heat to help kill mites and their eggs. We have had many customers use the above recommendations with great success. Most customers report that it can take several months to get rid of all of the mites.
Onslaught Insecticide can be applied to listed interior crevices once every 90 days. According to the product label, when treating crawling insect pests indoors you are able to repeat application as needed but do not exceed more than 1 application every 7 days.
We recommend using Onslaught, if you are treating the floors as well. Onslaught is odorless, dries clear and treats many different types of insects.
Onslaught Insecticide: Mix 0.5 oz of Onslaught with 1 gallon of water (+ 1 oz of Martins IGR if needed, please see below) to treat a 1,000 sq ft area. Thoroughly apply as a fine particle broadcast spray to infested rugs, carpets, and pet resting areas.