Well, we still need Caroline Chadwick's death cert. Until proved otherwise she was a Chadwick and not a Teal or a Hackney at the time of death.
The Ackney family that was a possibilty for Caroline's family did include a Margaret as a sister.
but - beware of two of the biggest dangers in family History. Firstly never ASSUME anything, things are not always as they seem, and secondly never take family hearsay as the ultimate truth. Always back up info as you go. Oh, and third one (!) done jump ahead too quick, confirm one person's details from as many angles as possible before leaping back generations.
Sorry, not meaning to nag or be a pain, but just want you to enjoy the hobby and not waste time and energy!
Looks like you have a fairly complex family situation here, so just work through it a step at a time. in fact I think there are really two issus on this thresd, the HAckney lot and the Booth lot. It may be worth you trying to separate them out a bit.