you need a lawyer
you need to think about 50:50 custody- it will happen if you want it to.
dont assume that "she gets the kids"- more and more the norm is for shared parenting.
Think about money, budgets and school locations etc- you might havwe to move further out to manage 2 rents - she might have to work FT
forearmed is forewarned OP- start saving
i have similar its depressing as fuck to live like this.
ps how can she just fuck off the Italy? once they are at school she wont be able to do that again!! I would document that and use it against her TBH (machiavellian I know) but thats fucking disgusting to do that
millions of people divorce and sucessfully share custody- you too OP
the fact you both work is good
and dont listen to your parents on this one 
but start to prepare a case NOW-
Boys in especial need their dads- I am reading "Raising Boys" and whilst some of it is hokum I 100% agree that boys need a strong parental figure growing up- unloess you are violent she cannot take your boys away- FACT
why is she threatening you? whats she so scared of you think? |I think understanding her fears might pave the way
she might well de depressed in the UK and want to move back to Italy, well tough titties- she gave birth here, and they Dad is a brit- she has no rights to fuck off home and thats whats probabkly upsetting her