I've got 5 red sexlinks and they are sweeties. Not sure how close you are to your chickens, but when you raise the new batch, handle them as much as possible, feed them out of your hand and if they misbehave , pick them up and stare at them for a bit. I did this with mine and they will crouch down when I reach for them and allow me to carry them around. Sure beats having to chase them. They follow me everywhere and 'help' me weed the garden.
Anyway, that did not stop them from trying to kill my new silkies on sight. I keep a piece of fence between them in the coop at night, but during they day they are fairly peaceful unless there is food involved.
It would probably be a good idea to raise the next batch with whatever other breeds you want all together, they will be less hostile to each other as adults. Good luck! Don't give up on the red sexlinks, they're wonderful layers!