What nationality are you?
I'm not sure if EEA visa is much easier than a UK fiancé visa...
For UK VISA:
She can come over using fiancé visa to UK then you two can marry in the UK within 6 months then apply for (FLR) further leave to remain as a spouse after getting married.
The thing with the UK visa, there's a financial requirement that the sponsor or you should earn at least £18600 a year. If you earn more than that and still supporting your kids, no problem at all.
I got married first here in the UK, then I reported my UK marriage to the registry of marriage in the Philippines. When I came back to Philippines, checked my marital status, it said that I am married. So that means marriage in the UK is recognisable in the Philippines (probably because I reported it? If not, I'm not pretty sure what would it be).
Do you not want it to be recognised in the Philippines for some personal reasons?
Anyway, about EEU visa, ask the other members here, Terpe might be able to give you some informations about that....
