HR not giving me a reliving letter as I resigned on probation period.

My company Head HR is not giving me a reliving letter after accepting the resignation the relived me from the service on the same day of resignation as I told them that I'm having some family emergency medical issues with my mother and I'll have to take care of her. The relived me on the same day. They're also telling me that they'll give me salary slips on the 7th March as the FNF salary will be credited on 7th March as per company rules. But she's denying to give me a propper reliving letter document. Sometimes saying that in our company reliving and experience letter are same. We cannot issue you a reliving letter for 2 months of service and all. But she gave 2 different letters to a employee who resigned one was reliving letter and other one was experience letter. I'll have to join another company on 3rd March. But the HR of new company is clearly saying I can't make you join without a propper reliving letter. My Head HR sometimes say company policy is that we don't issue reliving letter to those employees who resign on probation period and sometimes she says tell your new company HR to talk to me directly. Basically she is getting personal ego issues because she was not able to retain me. All my conversation was very polite and gentle all the time with all hr and management. Even my manager is not supporting me she's saying I can't help you it's HR's matter. Please suggest what to do in this situation. I'm very frustrated with all this shit she's doing just because of her personal ego satisfaction. What can I do she's doing it purposely so that can't join other company on time.