I have a database in which there is a parent \"Account\" row that then has a 1-Many relationship with another table, and that table has a 1-Many relationship with another table.
It sounds like you might have indexing issues.
Assume a parent-to-child relationship on column ParentId. By definition, column ParentId in the Parent table must have a primary or unique constraint, and thus be indexed. The child table, however, need not be indexed on ParentId. When you delete a parent entry, SQL has to delete all rows in the child table that have been assigned that foreign key... and if that column is not indexed, the work will have to be done with table scans. This could occur once for each table in your "deletion chain".
Of course, it might just be volume. Deleting a few k rows from 100k+ databases with multiple indexes, even if the "delete lookup" field is indexed, could take significant time -- and dont' forget locking and blocking if you've got users accessing your system during the delete!
Deferring the delete until a schedule maintenance window, as KM suggests, would definitely be an option--though it might require a serious modification to your code base.
A delete is a delete, and if you want to delete massive amounts of rows (100k), it will take a while.
If you do a soft delete (set a status to "D" for example) you can then run a job to actually delete the rows in batches of say 1,000 or so over time it may work better for you. The soft delete should update only the header row and would be very fast. You'd need to code your application to ignore these "D" status rows and their children though.
EDIT To further @Kane's comment. you could only do a soft delete, or you could do a soft delete followed by a batch process to do the actual deletes if you really want to. I'd just stick with the soft deletes if drive space is not an issue.
Have you indexed all the foreign keys? That's a common issue.