If you have private health insurance could you still be eligible for the GP only medical card? On the form it asks you if you have private health insurance (which may or may not cover part of GP costs depending which insurer/plan you are on). Don't want to go to all the trouble of filling the extensive form and supplemental documentation if we are not eligible.
I don't think having health insurance is relevant. Entitlement is decided by a means test, with allowances for mortgage/rent paid and childcare costs, AFAIK.