It sounds like you have an obstruction between the wash tubs and the outlet to your sewer line. Are the wash tubs in the basement and the sink you mentioned on the first floor, or are they both on the same floor? The chemicals usually won't fix things. If you do call a plumber, mention to him what you used. In my unprofessional opinion, you probably need to have the line snaked out to clear it. The washing machine pumps maybe 40 gallons of water in a few minutes; probably faster than draining a full tub. That is the first place you'll notice an obstruction usually.
If you have a septic system instead of city sewer lines, you may have other problems, but it could still be an obstruction.