Retailers that prevent children from entering with their parents may be brought before the Workplace Relations Commission (WRC) for breaching the Equal Status Act.
The National Public Health Emergency Team (Nphet) is being called on to reiterate that children are deemed low-risk when it comes to Covid-19 and stores have no legal right to ban them.
An investigation by the Irish Independent has found that several leading supermarkets are standing by their lockdown policy of "one person per family", first introduced as an emergency measure last March.
This is despite Nphet and Government officials stating that stores have not been advised to prevent children from entering and retailers should take a common-sense approach.
Lockdown has been a "nightmare" for lone parents and stores' anti-family policies are making it even harder, according to Louise Bayliss from Single Parents Acting For Rights of Kids (Spark).
She said at least three lone parents had been in contact with the WRC and planned to proceed with their complaints under the Equality Status Act.
A "really negative narrative" had surrounded children since the epidemic began after they were falsely listed as "super-spreaders" of the disease, she added.
Medical evidence has found they are in fact low-risk when it comes to spreading Covid-19.
Widower Stephen Teap raised the issue last week after being told he had to leave his two boys aged five and seven outside a SuperValu store in Clonakilty, Co Cork. When he objected, he was told the store had designated 'family-friendly' hours of which he should avail instead.
An Irish Independent survey of leading supermarkets found huge disparities between different stores and franchises.
SuperValu says it does not have a store-wide policy that children couldn't come into stores. "We do, however, in the interests of the health of our staff and customers, encourage families to limit their visit to one or two people per family where possible," said a spokesperson.
Aldi says it encourages 'one customer per trolley' to facilitate a "safe shopping experience for all our customers" but would not turn away any customer.
Family-owned supermarket Nolan's of Clontarf in Dublin said children were not allowed in its store except in a buggy or trolley, with an exception made for carers or assistants.
"Our staff members and customers have expressed concerns that social distancing is much harder to implement with children in the store," said a spokesperson.
Lidl says that it appreciates that "for a variety of reasons", not all parents could shop alone.
"For that reason, we have not implemented a one person per shop policy and we encourage shoppers to maintain a social distance at all times in our stores, as per the public health guidelines," it said.
The WRC said it did not comment on individual cases.