I got RIR the first time I raised chickens. They were great layers but I found them to be too aggressive to my Ameraucanas. I would not keep RIRs with the more docile breeds as I don't think that is a good combo based on my experience.
I'm surprised about your RIR's. I've got 1 in my flock and it's one of the friendliest. Now it will be the first to put another chick in it's place, but it's not aggressive at all. I'm wondering if the different experience just happens to be the individual personality of the chicken. I love my RIR. The aggressive one in my small flock is the Buff Orp.