>reset itself. If the 'on' lap between the relays is longer, no problem
>occurs. Any suggestion for this 'fast' start?

Have the PIC drive a transistor which can handle several times the current
required by the coil in the relay.  You might not be resetting the PIC, but
the relay might not have enough amps to flip to the new state reliably.
Often a large cap can be discharged through the windings to make this
happen quicker.

Do not update the pins directly.  Instead, update a "shadow" of the port,
then write the new value directly to the port.  This is standard practice
for reliable applications.

shadow_port     ds      1
#define relay_1 shadow_port,0
#define relay_2 shadow_port,1

...
        bsf     relay_1                 ; Turn on relay 1
        movf    shadow_port,w
        movwf   PORTB
        call    delay_50_mS             ; wait
        bsf     relay_2                 ; Do for relay 2
        movf    shadow_port,w
        movwf   PORTB
...

Andy