EU citizen with DUI conviction in US

I want to know if an EU citizen is allowed to travel to the UK if he/she was recently convicted of drunk driving -conviction occurred in the USA-.

It is quite embarrassing but due to an emergency I had to do a really short drive and I was above the legal limit of blood alcohol level. I got a DUI conviction in the USA about a month ago and will be done with all the payments of fines and community service soon. The conviction was a big fine and 4 days of community service.

I want to travel to the UK and I cant find information online regarding if I will be refused entry to the UK. I read that for non EU nationals it might be hard to apply for a visa. But I cannot find anything about EU nationals.

Final question: my spouse is a US citizen and if we relocate in Europe, say the UK, will she be denied a EEA family permit and residence card because of my DUI conviction?

Thank you.