Yes they have been living side by side for four weeks.The feed isn't an issue (solution: you put everyone on what the younger birds are eating), they're just at an awkward age to add to adults, too old for early integration, too young to stand up to the adults. Have they been in line of sight of the adults, i.e. living in a fenced off part of the run? That'd be the first step.
In separate coops and runs?Yes they have been living side by side for four weeks.