Firstly you will need to get an psri number when you arrive in ireland (same as national insurance number in uk) your children will need them too. Not sure what benefits you will be entitiled too, but will definitely need to get the number before you can even apply. This can take awhile. Ireland has the hse instead of the nhs, the major difference is you have to pay over here, you may be intitled to a medical card which will cover some of the costs but it is means tested. The average cost of seeing your gp is between 30-70 euros a go plus any perscription you might be given. This would have been completly free in uk. Under 5s visits to gp are now free but think the stiil have to pay full cost of any prescriptions. The health system as far as secondary care ie hospitals is very confusing, we have health insurance but very confusing as to what it actually covers, and you have to cover so much of the payment. Schools stsrt at age 5 and you are entitiled to one free year before this, this can be at a nursery or at certain creches. Schooling can be expensive also as you have to buy all you childs books, a friend of ours has three daughters an it cost them sround 2000euros for the three of them in setember!
As for looking fo work, the recession has hit ireland much harder than in the uk, unemployment is getting better but is still very high, so dont bank on getting work quickly, and wouldnt depend on recieving any benefits, you may be entitled but could take a long while, i would check on the irish govs website as to entitlements and time frames.
Ireland is a great place to live but everything is more expensive, getting work can be very tricky. Things tend to be done very slowly too, council buildingd/tax offices etc are only open one afternoon a week, which is very fustrating when you are trying to get things like psri numbers, benefit claims, medicals etc sorted. As you have family over here things could be made easier as they know where everything is, opening hours, lots of local knowledge. Ask them to go into places like the gp surgery, benefits place and collect any infomation they can to help you out, and give you a better understanding of things.
Hope this helps. :)