Mothering Sunday is the fourth Sunday in Lent and so, like Palm Sunday, Easter etc. is a moveable feast. Although I have never found any reference to it in 16th century records, Steve Roud in The English Year points out that it is mentioned in Robert Herrick's 17th century collection of poems, Hesperides (1648):
I'll to thee a simnell bring
Gainst thou go'st a mothering.
And in Richard Symonds' diary from 1644:
Every mid-Lent Sunday is a great day in Worcester, when all the children and god-children meet at the head and chief of the family and have a feast. They call it the Mothering-day.
So it was definitely celebrated by the mid 17th century.