As a Subcontractor under an Option A Subcontract, am I obliged to provide copies of the Sub-Subcontractors programme to the Contractor if I have incorporated them within my programme for acceptance ?
No. You only have to give a programme in accordance with the contract i.e. 31.2 and 32.1 (from memory, I am on hols).
If the mina Contractor wants any sub-Subcontractor programmes, then they would have to issue an instruction changing the Works Information (NEC3) or Scope (NEC4). That is a compensation event.