LB, I would not cover the sink year-round with contact paper, for a week it’s not bad, but more than that, it starts to peel off due to the almost constant contact with water. As far as using two bins, they might have one sitting on one counter next to the sink and the other one in the sink itself or on the other counter. When they wish to do dishes, then they put the bin in the sink and wash them. Or maybe they do the dishes without the bin at all, just use it to collect them in it.
When I designed my kitchen in an apartment that was as yet unbuilt, I paid extra to have a second sink put in and brought over large stainless steel sinks so that I could kasher them for Pesach. That is a near-ideal kitchen, but I could have easily spent less money and brought in ceramic sinks that I could not kasher for Pesach. Here in EY, they sell plastic insert for sinks for Pesach. But there is definitely nothing assur about using one sink or a not kasherable one.