That's not a viable option when the coop is currently occupied by 4 senior hens that are driving the pullets out because they have not been properly acclimated to each other. Locking them in will result in injury or death.
Can you please post pictures of the coop? The number one resource you need when integrating is SPACE.
You haven't given the hens nearly enough time to acclimate to the pullets. The 'look don't touch' portion of integration should be weeks and then it will take many more weeks before the flock...