Is there a good source for determining, once and for all, exactly how I am related to someone (like my mother's first cousin's grandchild, etc.)?

Your mother's first cousin's grandchild is your 2nd cousin once removed. Draw a family tree starting with the common ancestor at the top, and keep each succeeding generation on the same level, or distance from the common ancestor. Blood relatives on the same horizontal level (other than siblings, which are the first level from the common ancestor) are numbered cousins, with no 'removal' involved. The 'removed' part comes into play when one is removed from an equal level fo cousinship (cousintry ?). Thus the children of first cousins are 2nd cousins, and their children are 3rd cousins to each other. The child of one's numbered cousin is one's numbered cousin once removed. In the example you gave, your mother's first cousin's child ( the parent of the aforementioned grandchild) is your 2nd cousin, but your mother's first cousin, once removed [from her(your mother's) first cousin]. ANother way to check is to count the number of generations back to the common ancestor. If two people have the same number, then the following applies:
1 generation removed = siblings
2 generations removed = 1st cousins
3 generations removed = 2nd cousins
This is not easy to explain without a drawing, so if you make your own, consult it when reading this. It all falls into place then.

Doriangreyed is, of course, correct. You may (but only may!) find this site helpful:

http://www.janyce.com/gene/cousins.html

or this one:

http://www.cswnet.com/~sbooks/genealogy/cousins/cousins.htm

I hope we've helped between us.

A good genealogy program such as Brothers Keeper can determine relationships.

Thanks for the explanation DG! I was wondering about that too! (A drawing really helps!)