There are a couple of expressions I've encountered which have been applied to spanking situations although I believe that they can have broader meanings:
{1} "Putting him (or her) through his (or her) paces," which in general means him/her being required to carry out some function which he/she has been trained to do, but can also refer specifically to him/her enduring corporal correction;
{2} "Sorting him (or her) out," I believe it's a British expression which generally means resolving behavior issues which he/she is experiencing, yet it usually seems to be in reference to accomplishing that via bottom-smacking chastisement.
In Texas and the American South, there's little doubt what retribution a miscreant is facing when sentenced to "a good and proper hiding" or "an old-fashioned country lickin' (or whuppin')"...

--C.K.