there is no problem claiming for step children,
its years ago since we claimed, but i'm sure there were a couple of boxes asking if the misses was subject to immigration control and also who was making a claim, i just ticked the box i was.

passports and birth certs i can understand them asking for that as they will have no UK records for your wife or step child.

your step child is a dependent of your wife, i wouldn't worry about it, if you ticked the boxes on the application that you was only making a claim and your wife was subject to immigration control and also to make double sure, make sure the money goes into your bank account