I feel that dms could cause them to ban your account?
I don't send DM's but share about retweets stats in a few hours.
So the child accounts just retweet and like?
Yes, but as @praetserge mentioned, it would be weird if you make them only interact with your mother account. Try to emulate a normal human behavior as much as you can. Follow multiple big/medium accounts in your niche and other niches, etc..
But mass retweeting without follow/unfollow, would it increase reach?
I don't mind the reach on those accounts as long as they are niche targeted, you can use them to generate engagement in your main account. They will gain followers if you make relevant non-spam comments tho.