I'd suggest you start here.
http://www.inis.gov.ie/en/INIS/Pages/im ... ion-finder
The ideal situation would be if you or your husband had an Irish-born parent or grandparent, which would allow the one with such heritage to claim citizenship.
Barring that (and I am no expert) it would seem your options are limited.
You don't qualify for a Stamp 0 visa, which would allow you to live in Ireland. But that seems geared toward retirees, or others of independent means. Your income level is probably enough. But you aren't allowed to work or engage in a profession with that visa.
http://www.inis.gov.ie/en/INIS/Stamp%20 ... mation.pdf
Anyway, it appears But there is no path to naturalisation with the Stamp 0 visa. And you can't avail yourself of State benefits. So even with sufficient income, that would seem to rule out school for your children.
It appears that all the visas that could allow you to become a naturalised citizen either require you to have a work permit, or to make a sizable investment in the country (€1 million, not financed, and committed for three years). If you are self employed or employed by a firm that is not in Ireland,a work permit seems unlikely.
You might want to contact INIS or the Irish Consul in the US, as yours is a situation that doesn't seem to fit their typical visa/immigration scenarios.
