You need to build the email Notification on the table being changed, so this is the child table. But you can use any words and fields you like in the custom email Notification, including any lookup fields which you bring down from the Parent Record.
You can build a hyperlink in the par3nt Record and ghis n look that up to use in the email Notification.
The format for that field in the Parent would be a formula rich Text field
var text URL = urlroot() & "db/" & dbid() & "?a=dr&rid=" & [Record ID#];
var text Words = "Link to Case";
"
" & $Words & ""