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.
Mother’s Day is a day in honour of the Virgin Mary as the Mother of Jesus, but was always mid Lent. The Day is also called Simnel Sunday and you bake a simnel cake to mark mid Lent. There are a variety of recipes, some with fruit, others much sweeter, others bitter or mixed. On Mother’s Sunday originally you made a feast in honour of Our Lady and served all of the women in the village or parish. The meal and gifts were made by all of the men for all of the women. Now we honour our mothers but we still give thanks for the family and honour Mary. I don’t think many people still make a simnel cake.