I was denied a visa on my dutch passport, what now?

you have to apply for a B-2 tourist visa

you may be denied that as well ... they are down on overstayers

but it may go smoothly

Your kids need to go where you are if they need to be with you.

If you have a spouse who is an US citizen the spouse can sponsor you for a greencard, but it's probably going to take a year until you get it.

You cannot live with ESTA in the US. You are also unlikely to get a visitors visa to join your family in the US because you will be seen as most likely to plan to overstay that visa. Which means that you would need an immigrant visa (greencard) in order to enter the US if the rest of your family lives permanently in the US.

Read up on immigration rules and try to follow them. That might take longer initially but will save a lot of time and trouble later.

On the site below it talks about being denied entry and what you can do.. My fiancee got denied because of an unfair reason of "not enough times to canada" which was not true because he had just as many ties to canada as I do to the states and I am still able to go into canada.. the countries all don't like international dating because they think everyone whos dating is trying to live in the other country "illegaly" so they get fussy alot.

http://www.visaplace.com/usa-immigration/denied-en...

How come your kids are in a country that you are not resident in? Are they with their other parent? if yes, then there is nothing that you can do except apply for another visa and be very apologetic about overstaying last time.

What you need to do is to have someone in the US put your kids on a plane to you.