I don't fancy the Kick Start plan. The VHI One plans are half price for kids and fourth and subsequent kids are free. If it was me and I'd probably put the first three kids on One Plan Complete (€168 each) and the youngest on Company Plan Executive (for free, and "should" refund €40 for routine dental and €75 for A&E, amongst other things). One Plan Starter @ €572 looks as good/bad as Kick Start for you, but you should be able to insure the kids with VHI and yourself with Laya (Essential Health 300 may suit you @ €933) [broken link removed]
snowyb will likely unearth better options for you if you supply your renewal date.