A level 2 VRQ in nails is usually a year long course so I’m not really surprised they won’t recognise a 2 day Nail course.
Did your trainer not recommend a linked insurance provider as usually, the short course companies purchase accreditation from a specific insurer who agrees to provide insurance cover to students who have successfully completed the course.
If your training doesn’t offer this then maybe you need to think about re-training with a leading brand such as OPI, CND, Young Nails etc. or complete a nationally recognised qualification via the college route.