SO if you know one of your dogs eats wood, why put down wood mulch??
Can the dog you have that eats wood be trained to not eat wood?
Quite frankly most wood products that are available from the garden store have some checmicals on them, like fire retardant.
How big of an area are you considering? There are other alternatives to wood mulch including, stone, rock, ground cover etc...

mazer, I am against using the wood mulch, but my husband insists. I thought maybe there was some kind of wood that was not toxic, but I guess I am wrong. I will keep pushing for another kind of mulch, but I'll bet you anything I lose! Then when the dog gets sick he'll complain about the vet bill. Thanks for your reply mazer.

deel, I just spent over $400 because my dog swallowed just a couple of tiny pieces of mulch!!!

What about pine mulch? Probably much less tasty.

I think murraysmom's idea of pine mulch is a good one. As with bark, it uses up some nitrogen when it decomposes, so a little extra fertilizer might help in some plantings.

A layer of composted mulch will break down over time, attracting earthworms and improving soil fertility - I put down 2-3 inches each spring and my roses are happier.

There is a mulch product made of cocoa bean hulls which I would warn against -- if dogs eat it they can become very ill, just as when they eat chocolate.

You need to make certain any mulch you get is not treated...it is very important. Placing any wood mulch will ultimately act as a help in retaining water, but for the first couple of years, the wood will actually pull moisture away from plants, sucking up the water until the cellulose breaks down....contact your local gardeners guild or agriculture department to see if youcan get some organic mulch...even a tree removal service might be able to deliver a load to your home for free, tel them what you want and you will be saving them a trip to the dump, just be certain it is pine, and not mixed....eucalyptus cuttings have loads of oil in them and are not so desirable. Good luck