My reporting manager and functional head isn't approving my resignation as I've requested for early relieving

I work in a limited company. My actual notice period is 2 months and I've asked for an early relieving in 1 month. The reason being mentioned is relocation as I'm moving to abroad with my family. Initially, when I discussed this with my reporting manager, she approved it verbally and asked me to raise my resignation through the system and I did so. But after a week, my reporting manager along with my HR SPOC, told that they cannot accept my early relieving as there are a lot of dependency on me and my manager brother's wedding is nearing and therefore I'll have to manage everything during the manager's absence. Note: I'm not in any managerial position inside the organization and I don't lead a team. Now, they are demanding me to submit a flight ticker as proof to approve my resignation. All this happening as my functional head is not approving my resignation and pressuring my manager to make me stay and complete my notice period. My functional head knows that my manager isn't capable of handling everything alone. [Note: Once there was no manager for this team, after just two months of joining this organization my previous manager left in just 15 days stating health reasons, and I was solely taking care of the team activities] But now my functional head and my manager is saying that without me it would be difficult for them to manage all the activities. However, I had a word with my HR head and they said I don't need to submit any proof. But still I need my manager and functional head's approval for early relieving which they are not ready to do. My functional head and reporting manager are close as they come from the same location and background [I don't wanna get into all those details now]. As per my appointment letter, given below is the clause mentioned with regard to notice period: 5. Notice Period on Resignation / Termination: This offer of appointment is based on the information furnished in your application for employment. This offer is subject to and conditional upon completion of pre-employment screening check. At any point of time, if it comes to the company’s notice that you have made any false statements or you have suppressed any information including in relation to your past services or other records, your employment may be terminated immediately without notice. All confirmed employees have to mandatorily serve the notice period of 60 calendar days from the date of submission of resignation/termination. For all employees on probation, the notice period is 15 days from the date of submission of resignation. Accrued leave cannot be adjusted against the mandatory notice period. Shortfall in the notice period shall be compensated by the party providing the notice (of separation or termination as the case may be) by payment of an amount equivalent to the basic salary payable for the notice period not served and the payment shall be before the last date of separation/ termination. Kindly advise