Please accept my condolences on your's grandmother's departure.
It is unfortunate that no rites were done just because she didn't have a son. I have to address this first before talking about prayaschitta.
In his book "Pithru Poojanam" (there is no online link for this book, sorry), Brahmasri Rajagopala Ganapaadi has mentioned a hierarchy of relations who are duty bound to do the apara karma, in this order:
Eldest Son, grandson, great grandson, adopted son or son's sons or son
who was given in adoption, daughter's son who will inherit the wealth
of deceased (Dhanahaari Dhouhitrah), daughter's son (who doesn't
inherit anything), wife/husband, daughter, own elder brother, own
other brothers, sons of brothers, sons of paternal uncles, father,
and so on for a total of 35 relations.
If there is no son, as in this case, the family has to find someone from this hierarchy who is willing and has faith (shraddha) to do the Shraadham. This is important since the same person will also have to do the yearly rites.
The author also mentions that for karma that was not done or improperly done with major flaws (or as in this case, not done at all), there is no recourse except redoing the karmas. For minor flaws or in addition to redoing the karmas, the author recommends:
- paaraayana of Srimad Ramayana for 9 nine days
- paaraayana Srimad Bhagavatam for 7 days.
- Respective Veda paaraayana through qualified scholars
- Bathing in holy rivers after proper sankalpam for the sathagati of the departed
- Donating black till/sesame seeds or rice with sesame seeds or black urad dall to impoverished people
- Donating dress or food on the maasika days to poor people
- Donating food and dress for laborers
and so on.
(Read this story of Dundukari's liberation by hearing Bhagavata Saptaha)
All said and done, based on one's veda, shakha and sutra, one needs to take advice from experienced scholars/priests and get the right person from the family to do the karmas (either in the elaborate fashion or as per capacity) and then do the activities like paarayana and dhaana etc.