I would think it unlikely that Ofsted would accept that. It is certainly not a qualification, as it does not have a QCF reference and does not appear on the OfQual list of qualifications. So please do not consider this training to be anything like a level 3 NVQ, NNEB, or anything like that.
Ofsted might accept it as Common Core if it can be clearly shown to have covered enough things. Ofsted says "If you are confident that you, or someone you intend will work with children in your childcare provision, have had training in all of the Common Core areas you can apply for registration on the voluntary part of the Childcare Register."
Personally I would not take the risk, instead get them to do a common core course that clearly says it does meet the requirements. Perhaps if you are really pushed for time, complete the paperwork with the current training and signup nanny for a course where the provider says it is suitable as a backup - such as BabyEm, MNT.
Ofsted will not accept an old CRB. CRB checks are only valid on the date of issue. So a DBS check will be needed. The only exception there may be to that is if the current CRB was issued by Ofsted due to the person being previously a Registered Childminder or Nursery Manager. Then they might fast track it but I would suspect they would still want a more recent check done.
These questions are best asked of Ofsted via Email. They will need full details from the certificates and they may not give you a definitive answer.
From what you have said, I would assume a DBS check is needed and suitable training course is needed.