It has been my experience that "dusty" hay is almost always moldy.... its the mold spores that you are seeing as "dust".
But I think your problem is not the dusty hay (mold or not) I think it is that your horses are more accustomed to eating the far more palatable Alfalfa and don't want the grass hay. I have had the exacgt same problem many times. I have TBs and it is pretty much custom to give them alfalfa (at 12.00 to 25.00 a bale)
On the occasions when my hay suppliers are out I get them a really nice quality grass hay that is fresh green and beautiful. They wont touch it EXCEPT to sleep on it. They rake it up in a pile and lay down on it!!
I'm with Beausant as far as the "who will cave first " game. Its me sadly
So be a good horse mommy and go spend your retirement money on some GOOD horse hay for your babies LOL.