There are a number of related, now-obsolete terms that Shakespeare might have used, all related to the Latin orbus meaning bereavement. These include most notably1
† orbity, n. Obs. A bereavement, esp. the loss of a child; the state or condition of being bereaved. Also (esp. in later use): childlessness. [Attestations from 1597 to 1804]
† orb, adj. Obs. rare. Childless. [Only two attestations, one in 1607—spelled orbe—and one in 1660]
Neither of these is an exact parallel for terms like widow or orphan, however. Interestingly, the latter of these shares an Indo-European root with orbus. Perhaps Shakespeare could have coined a parallel term orban for parents bereaved of their child(ren).
Alternatively, some compound term might work; perhaps something like orbe-
mother for a bereaved mother.2
1 Definitions from the Oxford English Dictionary: OED Online, Oxford University Press, March 2017.
2 Other possibilities, but these are pure invention: orbant or orphent, combining orb or orphan and parent; orbither, combining orb/orbity with mother/father.
Unfortunately, many possible options are problematic for modern English-speakers, due to the similarity to the unrelated words orb and orbit. One possible solution would be to stick closer to the Latin, for example mater orba or orba mater. A question on the Latin SE might get more plausible suggestions along these lines.