In law, an employee with a child under the age of 6 can request to work flexible hours. The application needs to be in writing stating that it is being made under the statutory right to apply for flexible working. It sounds like you had verbal discussion about it, but never formalised it in writing. The fact that you then chose to resign means that you ended your right to make a request for flexible working.
However, your employer then offered you a revised job verbally and therefore in effect rescinded your resignation letter. Therefore a legally binding contract has been made again between you and your employer (it is still binding even though only verbal) so they cannot withdraw the offer and accept your notice. Therefore in theory you are still employed at this Company and if they wish to terminate your employment contract they will have to follow legally laid down procedures.
The fact that your employer is contacting you each time on Facebook rather than via mobile also seems unprofessional and inappropriate.
I would suggest that you pursue an internal grievance with your employer using the statutory grievance procedure if your company does not have its own grievance procedure.
Simultaneously, you may also want to seek some further legal advice around your situation since you might have a case against your employer for constructive dismissal (because your flexible working request was not initially honoured) or potentially sex discrimination.
Whilst every care has been taken in compiling this answer, WorkingMums cannot be held responsible for any errors or omissions. This information is not intended to be a substitute for specific legal advice.