Pico laser penetrates the skin to kill off the melanin that causes these spots. Conversely, chemical peels remove the top layer of the skin to stimulate the growth of a new layer of skin [1]. Pico laser and chemical peels treat sun spots, wrinkles and hyperpigmentation and improve skin texture/tones [2]. Pico laser, however, is preferred when removing tattoos.
If you are getting both, an interval of 2 weeks will be sufficient for the skin sensitivity to subside. Alternatively, do the chemical peel first, then followed by the pico-laser 2 weeks later. In this way, the effects of the pico-laser may be enhanced after the skin has been refreshed by the chemical peeling.
References:
1. Landau M. Chemical peels. Clinics in Dermatology. 2008;26(2):200-208. doi:10.1016/j.clindermatol.2007.09.012
2. Weiss RA, McDaniel DH, Weiss MA, Mahoney AM, Beasley KL, Halvorson CR. Safety and efficacy of a novel diffractive lens array using a picosecond 755 nm alexandrite laser for treatment of wrinkles. Lasers in Surgery and Medicine. 2016;49(1):40-44. doi:10.1002/lsm.22577