Her parents, grandmother and daughters - one-year-old Emma and 10-week-old Grace - chose to have lunch at Bonapartes in the city's Queen Street Station, partly because it had a children's menu.
After arriving at the restaurant, and struggling with a double buggy, Heather settled the girls.
But moments later a waitress told the party of six they wouldn't be served - because Emma and Grace were too young to hold a knife and fork.
The mum hoped Emma would eat chicken nuggets and chips with her fingers. Heather, a single mum who was being treated by her gran Sarah Stewart, 61, for her birthday, said: "We had just sat down at the table when the member of staff told me that because neither of them could hold a knife and fork they were not allowed to be in."
She added: "I was so embarrassed."
The family claim they were told the rule was a condition of the venue's licence.
Today, a member of staff at Bonapartes admitted it did have restrictions on serving young ones.
She said: "We do serve children, but it depends what age.
"We must follow regulations under the Children's Act and the licensing law."
When one of our staff posing as a parent phoned to inquire if she could bring her children in, a member of staff said the youngsters would have to eat something and they would have to eat it with a knife and fork.
When it was suggested this was quite an unusual policy, she replied: "It is part of the licensing laws in Glasgow and there is no way round it."
But a licensing expert from Harper Macleod solicitors, which represents licensed premises, said today she had never heard of such a condition.
She added: "If it is a restaurant with a restaurant licence, children of any age can eat there, whether they can hold a knife or fork or not.
"The licence holder has the right to refuse service if kids are playing up or are rowdy, but there is no law or condition saying that you can only be served if you can hold cutlery."
There is no knife and fork condition that can be or has ever been issued by the Licensing Board, despite the premises claiming there is.
Councillor Malcolm McLean, a member of the board, said: "I have never heard of that and I am not aware of any such thing. This is nonsense."
