Is this enough to prove that she will be going back after her visit?
No, at least it doesn't look that way to me.
The authorities will want to know how your mother supports herself, if she is unemployed, does she have other sources of income (pension, investment income, remittances from offspring, other).
They will want to know what ties she has to Serbia that will make it necessary for her to return there.
When you apply you’ll need to provide:
- a current passport or other valid travel identification
- evidence that you can support yourself during your trip, such as bank statements or payslips from the last 6 months
You’ll need to provide the following:
- the dates you’re planning to travel to the UK
- details of where you’ll be staying during your visit
- how much you think your trip will cost
- your current home address and how long you’ve lived there
- your parents’ names and dates of birth
- how much you earn in a year
You might also need:
- details of your travel history for the past 10 years (as shown in your passport)
- your employer’s address and telephone number
- your partner’s name, date of birth, and passport number
- the name and address of anyone paying for your trip
- the name, address and passport number of any family members you have in the UK
- details of any criminal, civil or immigration offences you have committed