It's hard - really impossible - to answer your questions without asking some questions. What part of the country would you be living in? How would your family be making a living? Do you all speak Spanish?
Your choices for schooling would probably be home schooling or expensive private bilingual schools. In some parts of the country, there aren't many or any private schools. The public schools do not offer a good education and some of the private schools aren't a whole lot better. You have to think that probably your children are going to want to return to their country at some point for college or work, and a poor Honduran education could put them at a great disadvantage.
Medical care is similar. Public health care is atrocious. There are some good private hospitals but those are going to be in the larger cities. In parts of the country there aren't even doctors or clinics available. The medications that you need may or may not be available in pharmacies. Generic drugs made in Central America generally cost much less but may or may not be the exact equivalent.
The cost of living really depends upon how and where you want to live. It can be less but some things cost more, like gas (close to US$5/gallon), electric, and American products. Housing is generally cheaper. You'll have to apply for residency for yourself and your children which will cost at least a couple of thousand dollars, maybe more.
This is a major life decision, not only for you, but for your children. I always recommend that people come down for a long (several months) visit before deciding. In your case, you really need to find out about medications, health care, and schooling in the area where you would be living.
