Bi-directional High Side Load Switch Design
One way to check your design is to see how the pro's do it.  Linear Technology (now a part of Analog Devices) has a line of power path controller chips that drive external power MOSFET's.  To be fair, some use your arrangement with the two drains connected.  but most have the two sources connected.  This eliminates the need for D2 and D4, so there is more gate voltage for enhancement.
Here is a link to one of their datasheets.  The circuit on the front page shows the FET connections.
https://www.analog.com/media/en/technical-documentation/data-sheets/ltc4418.pdf