Best route from Malibu to Palm Springs

Lots of luck with that. There really isn’t a traffic free route between Malibu and Palm Springs. That being said, I would simply go east on PCH to I-10, CA-60, then I-10 to the Palm Springs turn-off. Or you could simply stay on I-10 the entire way. On a work day, I would try to leave Malibu about 9 am to at least avoid the rush hour traffic. But you will still have lots of traffic, especially until you get east of downtown Los Angeles.