I am doing similar. Using a 1/0 AWG from the main panel to subpanel which are next to each other. From there 2AWG SER cable to the WC and 6AWG to my existing Clippercreek HCS60.
Just as a quick reminder: #2 copper SER is not good for the 80A charge setting (100A circuit) if it passes through or in any insulated walls, as it's only good to 95A in that case. NEC 338.10(B)(4)(a) says "Where installed in thermal insulation the ampacity shall be in accordance with the 60 degC (140 degF) conductor temperature rating."
If it's in a surface-mounted conduit or used as exposed cabling (with an appropriate sleeve where "subject to physical damage", generally below 7'), you're fine.