I presume you are using the add Child button which is sitting on top of the embedded report of children on the parent form.
One option is to edit that report element so that it does not show the add child button.
so deselect
Show create record button
Then put the add child button on the form directly and change the code to comment out the last part so that the code it will look like this.
URLRoot() & "db/" & [_DBID_CHILDREN] & "?a=API_GenAddRecordForm&_fid_7=" & URLEncode ([Record ID#])
//& "&z=" & Rurl()
That way, when you save the child record it will land the user in View mode on the child record