FWIW... I have two y-valves too. I attach my drinking water Y-valve to camp supply, with one hose going to my RV's water supply, and the second usually to a second white drinking water hose that I feed under the RV to the other side where I cook, and I use that to fill cooking pans with water and for cooking. When I'm doing the black-tank rinse, I remove that Y-valve and attach a different "black" one that feeds (1) my tank rinse mechanism that the OP is concerned about, and (2) my Sewer Solution feed (Valterra product). Even before I needed that Sewer Solution feed , I never felt comfortable mixing my black and white hoses. Period. So one y-valve that feeds both black and white supplies just won't pass my gut check.
2013 Fleetwood Discovery 40G, Cummins ISL,Freightliner Chassis, Allison 3000.
2017 Ford F150 Lariat toad w/
Blue Ox Aventa tow bar and M&G Braking System