It is undoubtedly a very good idea to include your children in any plans you have for relocating to Ireland. Take them with you on your fact-finding or house-hunting trips. When you do relocate, take the time to listen to what they have to say about their new school and friends. Keep track of their progress in their new school. If your children are very young it might help ease their tensions if you accompany them to school for the first few days.
Bringing your children to Ireland isn't likely to produce any major problems. Crimes against children are rare. Depending on the age group, kids in Ireland face the same sort of problems at school as they would in the United States. Although there is little danger of a child turning up at school with a gun, you do get instances of bullying and of high school kids being targeted by drug dealers.
If you have very young children and intend to work here, then child-care will be important. Unfortunately, at the moment, crëche facilities in Ireland can only be described as abysmal and expensive. In Dublin, if you can find one with spaces, a crëche is likely to be charging €100-150 ($124-186) a week.
Other than basketball, your kids will have to get used to a new set of sports. Gaelic games are popular, as is soccer, but there is little in the way of tuition in sports such as tennis. You would need to arrange that privately. Teenage culture will not be much different either. Most of the U.S. rap stars are popular here as well. One potential problem you will have to keep an eye on, though, is teenage drinking. Ireland does not have the same tough laws as some U.S. states. Although a voluntary prove your age card system has been widely adopted by publicans, teenage drinking remains a problem.