Hello, and welcome to BYC. Kids and chickens are possible following normal sanitary procedures and monitoring all interactions. Kids can inadvertently injure chicks/small birds.
I would integrate all 3 at the same time. 'safety in numbers' when dealing with the home team. If they are in pens 5-10 feet apart, both flocks are already exposed to anything the other flock may have so integration can take place at any time.