If you only have one coax jack, unfortunately, you can't use MoCA. The connection needs to get into the router and then out over Ethernet before a MoCA adapter can work its magic.
However, if I'm understanding your diagram correctly you don't need MoCA to do what you want. All you need to do is connect one of the mesh units to your existing router with Ethernet. Then you can put the other ones wherever you want them, and it'll work like your second diagram. Optimally, you would want to put your existing router in bridge mode, but it may not support that if it's ISP-provided gear (many don't).