one way gates work the best for me, but really I don't think you will have too much problem, you older birds, are not that much older, and there will be a size difference, but not a huge size difference, and you are adding equal to equal numbers, 3 head to 3 head... All should go pretty well unless you are drastically short of space, and you might be.
A lot of pre fab coops say they will take 6 birds, but really are only big enough for three. They may still get along, if that is what you have, now, as none of the birds are full grown, but may start to create problems later in the fall and winter as they all will be full sized, and roosted for the long winter nights.
It is kind of amazing how what seems like more than enough room for chicks rapidly becomes not enough room for hens. So if you measured, and have ample space, I think you would be good to go. If you start having problems later on, might be not enough space.