When I type I can use both my hands almost simultaneously. I can now write in script simultaneously if I write with the left hand right to left and the right hand left to right. I pay attention to the left hand and sort of let the right hand do it's thing. If I get a little excited or nervous it breaks down and both sides suffer. It feels like that I switch my attention back to the right or normal way and leave the left stranded and then I try switching back quickly and then I am out of sync. I wonder if that is what stammerers go through with their voice, or in my view their tongues. A confusion of dominance in their minds.
If I try to write both hands left to right I my left script suffers. If I try to write both hands to the left my right hand tends to write the letters on top of each other. I can write either hand in the opposite direction by itself.
But the best results and the most natural feel is for both hands to write away from midline simultaneously when trying with both hands. I wrote a couple of checks the other day with my right dominant hand and I have not had such good handwriting in forty years. Don't know why