Within the Quinn Healthcare range of plans alone, you've a number of options open to you.
One option is to put the children on either Essential or Essential Starter, both of which will cover the children for a semi private room in public hospitals. If they are admitted to a private hospital, you pay a portion of the bill yourself. I'm not sure exactly how much, but I think it's around €400 per night depending on what hospital.
Another option is to move the family to Quinn's Company Health Plus with Excess. As far as I can determine, this is near identical to what you have but an adult is €134 cheaper based on the current rates.
Another option again for all the family is to switch to Quinn's Essental Plus Starter. This is similar to what you have, but the biggest difference is that it doesn't cover as many private hospitals as your current plan. For example in Galway, it only covers the Galway Clinic and not the Bon Secours Hospital. The adult saving here is €233, but do be absolutely certain that you're okay with the hospital cover before switching. There's nothing wrong with the Galway Clinic (assuming you're in Galway), but if there's a particular consultant or particular treatment you want to have access to, make sure it's available in a hospital covered by your scheme.
Quinn's brochure for all the Essential schemes is online here -
http://www.quinn-healthcare.com/pdf/essbroch.pdf, so you can compare most of them side by side. The brochure for their Company schemes is here
http://www.quinn-healthcare.com/pdf/chbroch.pdf. Anyone can join a company scheme, so don't be worried about the name of the plan.
Finally, Quinn announced a reduction in the current child prices last week, but this probably won't affect you until you're renewal -
http://www.quinn-healthcare.com/press_and_media/pressrelease010710.htm.
Obviously VHI and Aviva have a number of plans as well, but I think once you've decided what kind of plan you want from Quinn, you'll be in a better position to look through what the others offer.