Coat of My Dream's Desire

The first page of my family tree book is covered in copies of photographs of my ancestors going back 7 generations. This book of my family tree concentrates on the Mennonite side of my lineage. Those ancestors were of Germanic (Dutch, Swiss, Austrian, German, Prussian) descent who lived in isolated colonies in what is now Ukraine. They were pacifist Anabaptists who were exempt from military duty.
In one of the photographs of my great great grandfather Jakob Martens's family, his three oldest sons (all under age 8) are wearing matching coats that look very reminiscent of a military uniform or something a Cossack would wear. To my limited knowledge of Mennonite culture and fashion of 101 years ago, this is ironic.
My great grandfather is the infant in the bonnet at the center of the photograph, which means that picture was taken in the early months of 1910, meaning they had already emigrated to South Dakota. Unfortunately, there is no one left alive from that family that I can ask about those coats I am so curious about.
I have been trying to research more about asymmetric wool coats of eastern Europe at the turn of the last century, but I have been finding a LOT of dead ends and irrelevant fodder. I speak Russian and a little Ukrainian, just as my ancestors did, so I've also been searching in those languages as well, mostly realizing I do not know enough fashion terminology, period.
I have realized that those beautiful uniform-like coats might be of purely unique design, because my father told me that my great-great-great-great grandfather Wilhelm Martens III was a tailor and lived to be 100 in 1919. He could have made those coats from his own design.
My ultimate wish is to have a replica of one of those coats made for myself. I have no idea how much that would cost, but I'm hoping I could find a tailor that can make one for under $300.
My other wish is to learn the very specific terminology for the definitive features of that coat. I know it is asymmetrical, but I want to know if there is a more specific term for it. I've started calling it a "right breasted" coat because it isn't double breasted, but the buttons are way off to the right. It has a sash-like belt that doesn't appear to have a practical function other than making it look fancy, and the collar almost appears Mandarin, but I am willing to bet it is something more specific than mandarin.
If I had a coat like that, it would go a lot better with my Russian fur hat. Though, after researching Cossack fashion, I decided that these coats are not likely inspired from Cossack designs.
I need a fashion guru!