In theory sounds good.
In Practise not so.
Your going against the immigration gradient. It is normal for Europeans to come to America to gain experience as an instructor not the other way round.
Do you have the right work on Europe already?
If no - then you won't get it as an instructor -there are hundreds of unemployed instructors in Europe!
You could instruct on a US registered aircraft in Europe, however to instruct on an EASA registered aircraft you would need an EASA licence and an EASA flight instructor(FI) rating. There is no conversion from the FAA CFI to EASA FI and rightly so - they are polar opposites in approach.
If you wanted to do your training in the US there is only one EASA FI school in the USA and the course is over $10,000 including accommodation. Before that you'd need the ATPL theory say $10,000-$12,000 including accommodation for 6 months plus the CPL conversion say $4,000 or so. Total around $25,000 by the time your qualified, but then you don't have the right to work there so why bother? Also why would you want to - there's a reason a huge percentage of EASA training is conducted in the USA - the weather isn't consistent enough in Europe so you just won't be able to make ends meet hence why there are so many Europeans instructing in the USA!
However, if you meet a cute European to marry and want to live there why not ;-)