Car Insurance says I Falsified NCD

I bought a car in 2016 and insured it with Quick Sure for the first two years and then in 2018 got a quote and insured it with Co-op Insurance. Quick sure sent me my Proof of No Claims and I forwarded it to Co-op.

At some point Co-op validated the proof of NCD with Quick Sure who told them it wasn't genuine. Co-op voided my insurance 13th April saying my Proof of NCD had been falsified. I checked the NCD proof that QS had sent me and it said 9 years NCD, I don't have 9 years NCD, I've had the car two years and the policy two years. I went online to my old QS account/dashboard and found a Proof of NCD - dated the same day as the one I requested 'thank you for requesting proof... etc' stating I had 2 years NCD. My schedule of Insurance for both the years I was with QS (2016 and 2017) states I have 1 year and then another year's No Claims, adding up to 2 years. And when I requested a quote from Co-op I told them I had 2 years NCD. I have had QS confirm to me in writing on (16th April) that I had 2 years NCD yet in separate correspondence with Co-op on 17th April they reiterated to them that the 9 years NCD document was not genuine.

I have asked QS to look into this, and have contacted the Financial Ombudsman who agrees with me that Co-op should accept my 2 NCD years proof as I have multiple instances of evidence that show I have 2 years NCD.

Co-op are insisting I get QS to acknowledge they made a mistake by saying the 9 years NCD document was an error they made, the Ombudsman said that the fact it's an error is inherent in them emailing me to confirm I have 2 years NCD but in the light of their most recent iteration that the 9 years NCD document is falsified Co-op won't un-void the insurance.

My questions are:

I have a 2nd car, insured with a different company, can I drive that?

Can I drive other people's cars third party? assuming they're fully comp (as am I on my 2nd car)

Also, can I add my uninsured car to my other policy without declaring its been made void?

I've lost several days work because of this and it's looking likely I will lose more, I will be raising a formal complain with both insurance companies as suggested by the Ombudsman and am likely to ask for compensation for lack of earnings and distress.

Many thanks for any help you can give me