Visa/Marriage advice needed?

Visa/Marriage advice needed?

Ok, so a quick summary of the situation I am in:

1. I am UK citizen.
2. My fiancee is US citizen.
3. We have 2 daughters together (Aged 3 and aged 7 months)
4. We have been friends for 12 years.
5. In relationship for just over 4 years.

Now, the situation we are in, when I used to visit the US, on the VWP green card, I mistakenly selected 'no' to the question “Have you ever been arrested or convicted”. I had been arrested of a sexual crime (Met a girl at a pub, turned out she was underage), but only cautioned. The caution has since expired. Through this misunderstanding, I am now no longer able to visit on the VWP. So am now unable to see my fiancee and kids, over 12 months now and I have not even seen my second daughter yet. We decided it would be best for us to get married and settle in the US, so we applied for the K1-fiancee visa, and they denied it due to misrepresenting myself on previous entries, but we are now applying for the waiver. We have enough sponsorship, but money is tight for us at the moment, so she has not been able to visit me with our daughters (They will be here in November this year visiting for 6 months).

Ok, so after all that, my question is, when she visits here, are we able to make a hop into the EU and just get married? As this is getting extremely frustrating and the US Embassy is taking a long time to communicate with us and always requesting more and more information, paperwork and fees. We just want to get married, be able to settle down and start living our lives together as a family. So, are we able to make a return trip into an EU country to get married? If so, which one would be the easiest for us?

Many thanks for any help you can all give us.

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