ARRRGGG, this is kinda getting nuts. If you want your PIC output 1 second high/low pulse to sit right on a rising edge of the 10 MHZ source any better than it already does, just put the PIC output to the data in of a 74AC74 D-latch flipflop and tie the flip-flop's clock input to the 10MHz source clock.
Running a cheap loop in the pic to count the equivalent of 5 million clock ins, output high, another 5 million clocks in and output low, without any PLL or timer is a brainless trivial piece of loop code in assembly. No PLL, no timer, no watchdog, no interrupts, no special sleep cycles, nothing else needed, it will just run without fail. Making the code pulse the output pin high/low as quick as it can after every 10 million clocks is the same 10-15 lines of assembly code.