var text URL= URLRoot() & "db/" & [_DBID_CHILD_TABLE_ID] & "?a=API_AddRecord&_fid_yy="&URLEncode ([Record ID#])&"&apptoken=zzzzzzzzzzzz&_fid_xx="&URLEncode(Today());
"javascript:" &
"$.get('" &
$URL &
"',function(){" &
"location.reload(true);" &
"});"
& "void(0);"
You will want to replace the "zzzzzzzzzz" with your app token,
change the fid_yy to the the field id of the [Related Parent] field on you child table.
and the fid_xx with the field id number that you are looking to right the date to.
If you have trouble, copy your current equation from your "Add" button, and post it here (possibly as a new question because this one it getting long), and we can help you out.