The incident involving Lady Flora actually occurred the year after Victoria's coronation, not during the same month as depicted.
Lord Paget entered Queen Victoria's service as her equerry in 1846, nine years after she was crowned. He held no position at court before then.
Even if the Duke of Cumberland was still in England (which he was not, having relocated to Hanover as its King), as an active member of the House of Lords, he would have no place in the Commons during its deliberations.
The Duchess of Kent complains about being relegated to the northern wing of Buckingham Palace. But the sun is shining directly through the windows which is impossible on a northern side.