HK cross border travel

I don't think your dad can enter mainland China freely with his HK ID card. He needs a home return permit.

I'm afraid it's not feasible to change the double-entry to a multiple-entry. You can apply for a new one in HK after the current one is used up. From HK to Futian checkpoint, you can travel by bus or MTR to Lok Ma Chau, then pass the border check to Futian side.

"Under the Easy Travel Scheme, holders of Hong Kong identity cards bearing "***", "*" or "R" symbol or locally issued Hong Kong permanent identity cards, who are aged 11 or above, can travel from Hong Kong to the Mainland and Macao SAR and vice versa without producing a HKSAR Re-entry Permit or other travel documents at any Hong Kong immigration control point. They are also not required to fill in any arrival card or departure card." www.immd.gov.hk/eng/service/travel_document/Application_for_HKSAR_Re-entry_Permit.html

I guess you referred is HKSAE Re-entry permit which means you don't need to show any document to come back to HK but you still need a permit to go to mainland.

My dad does have another card that says "This card is intended for its holder to travel to the mainland of China"