My brother sent me a message. It contained information that I would like my wife to have. Is there a way to add her to the on-going message or do I need to start a new message to my wife and retype everything?
Forwarding might be the easiest, else It looks like you can only start a new groupchat.
If you press and hold the message (or even picture) and select 'more' it will switch to multi select mode, so you can select more messages. You'll also find a forward button (right bottom for me) if you click that a new message will be created with the selected items. You then only need to set the recepients to send it.
If it is an iMessage thread with two or more other people besides you (ie 3 or more people total in the thread), then you can add another contact by tapping "Details" in the upper right corner of the thread, and then selecting "Add Contact"
If it is a Group MMS, then you cannot add other person. And should follow the responses above.