Is there a way to edit a record and add a record to another table with the same button?

This will work

$EditTask
& "rdr=" & urlencode($AddRecordOne)

However, be aware that if the user clicks that button to Create the 2nd child record manually and they get stuck by lightning or lose the internet or just get distracted and they never actually save the 2nd child record, then the original child will be already flagged as converted, but in fact was not.

I suggest a more foolproof method would be to make the 2nd child also be a child of the first child.  Then the 1st child can have a summary count field to know how many 2nd child children it has (it should be 1 if successfully converted).  So then the flag on the first child as to if it has been converted will be if the [# of 2nd children] >0.