I am working on a project that requires weaving wide strips of leather
into a basket weave pattern.  I'd like to have them two different
colors.   The strips are going to be wide, 1 to 2 inches, and will
have the sides exposed on alernating weaves.   Wetting the normal
vegetable tanned leather helps to tighten the gaps in the weave
pattern but I can I dye it first and then wet it?  If so, what are the
recommended products and will they leach when wet?

I don't know: but the easiest way to find out is to experiment on a
small sample of both colours of leather.