This whole arrangement is a complete pile of bogus shite by two dysfunctional people.
Nobody who had any genuine intention of fostering a happy extended family situation would entertain this.
Sending a six year old boy off with two adults he barely knows and his young teenage sister for the best part of the week is just awful.
It's unfair on the boy. It's unfair on his sister. It's unfair on the adult who has met the child once.
To ask a childless woman who has a teenage stepdaughter to take a small child she doesn't know, who isn't dry at night, into her her home for several days and nights is just taking the fucking piss.
When you marry a man with a child you don't agree to take on every new baby his ex creates in the future.
Extended families are not created by diktat.
People come to be fond of each other by spending time together in normal social situations.
A person who genuinely wanted to help this boy feel included in his sister's life would neither suggest this, nor agree to it.
A family day out near his home would be an obvious first step. Then his mother bringing him to stay nearby to meet his sister's cousins some holiday time.
But this imposition on the OP's goodwill is part of some unfinished business between the DSD's parents.
I would be looking for somewhere else to live if I shared a home with a man who carried on like this.
Nice guy my arse.
There is nobody more selfish that the vain person in love with their self-image of how "nice" they are.