It's a lot easier if your children are under 21 when they apply for family permits to join you.
If they are 21 or over then you would need to prove they are your dependants. I.e. they are mainly or wholly financially dependent on you or the EEA or that you lived together recently as part of the same household.
An explanation of dependency can be found at 5.1.2 here:
http://www.ukba.homeoffice.gov.uk/sitec ... iew=Binary
It's the EEA national who is the sponsor, so the EEA needs to prove they are exercising treaty rights in the UK and that you are their spouse and the children's mother.
More info about family permits can be found here:
http://www.ukba.homeoffice.gov.uk/eucit ... /applying/
Many topics on here are about the extra questions that are often irrelevant on the Vaf5 form.
