Do you have access to the raw data for your 2C1R (the shorthand I use for second cousin once removed in my spreadsheet)? If so, you could run David Pike's utility to compare yourself and your mother to the 2C1R. Every segment where you and your 2C1R match should be found in your mother. http://www.math.mun.ca/~dapike/FF23utils/pair-comp.php
Now you and your 2C1R could match the Hagler in different places, so this experiment doesn't necessarily prove anything for that riddle. It's just a way of confirming that things are proceeding in an orderly fashion for the three of you. If your Hagler connection is interested in pursuing this, his/her raw data would probably clear up the mystery.