We were hoping to get a child's name appended to the subject line in the FFW alerts, since families often have more than one child. If they submit three "Clothing Receipts" items, it's easy to see them as identical. But if it says "Clothing Receipts (Child 1)", etc., that would be great.

You can do this in the regular Email Alerts, so I'm voting for that option too!
All we need though in Organization Settings -> Organization Preferences -> Family Web -> Emails -> Inbound Notifications from Families is a check box "Append Case Name to subject line".