Terri McCue, from the South Side, is taking legal action because she says her 19-year-old son Andrew, who has Down's syndrome, is not being assessed in the right way.
Families across the city are accusing council chiefs of using a "tick box exercise" to assess their loved ones' needs.
After filling out the Self Evaluation Questionnaire (SEQ) with a social worker, mum-of-two Terri was offered £9500 a year to pay for Andrew's support needs.
She queried the outcome and was allocated £10,300.
However, Ms McCue says Andrew needs around £17,000, which would pay for 32 nights of respite care as well as other aspects of his care.
The 56-year-old grand-mother-of-one said: "I feel I've had no option but to take legal action on behalf of my son.
"In one of the SEQ questions the council said Andrew needed help once a week. But he needs help every day. If it's once a week then I'm asking them what day is it he needs help? Is it a Monday? Or a Saturday?
"It's just a tick box exercise and they are not taking into account Andrew as a person."
The first hearing is due to take place at the Court of Session in Edinburgh on May 9. The family is being represented by Tony Kelly of Coatbridge-based law firm Taylor and Kelly.
Ms McCue said: "I've showed them (the council) an itemised report of everything Andrew needs. The budget that will meet his needs is around £17,000.
"In the court hearing we'll be arguing that if you score people correctly they will get the amount they need."
The council says that self-directed support (SDS) policy is designed to give families and individuals choice.
It is part of personalisation, a new policy being rolled out nationally. The assessment is used to decide the budgets people are given for care.
Susan Aitken, SNP councillor for Langside and social work spokeswoman, said: "The McCue family are one of many across Glasgow who have found their budgets for care and support services cut to the bone after they have been through the personal-isation assessment.
"It is no surprise that, sooner or later, a family was going to feel forced to take legal action. Terri's case could have significant implications not only for her own family but for others across Glasgow who face similar struggles."
Helen McCourt, 49, from the East End, said accepting the budget of around £8500 that was allocated for her 31-year-old daughter, Laura, who has Down's syndrome, would drive her "deep into poverty".
She said: "We would end up having to go to a food bank. I'm refusing to accept it. I feel like Laura's been isolated and pushed out of the system."
The family were part of the group who campaigned to keep open the Accord day centre, which Laura attended every day. Ms McCourt said: "It affects the whole family - it's not just Laura or me."
However, Kim Kenny, 49, said the system was effective now for her 22-year-old son Jamie, who has autism. She said: "It is working for him at the moment but I am fearful of what will happen when Jamie is older."
A city council spokesman said: "The process used in Glasgow to assess people for personal social care budgets is both lawful and based on robust social work practice.
"It has been tested in the courts, supported by the opinion of legal counsel and is subjected to regular scrutiny by service users, carers, trades unions and councillors.
"We are always willing to listen to those with a stake in the system and will make improvements where necess-ary. However, we are fully confident the personalisation system is being operated appropriately in Glasgow."