Why can you all not accept that OP does not want to jump to the agenda being set on here.
She is married to her DH, she should surely be the one to set her own agenda. ?
Not everyone wants to know if their 'DH' or 'DW' is having an affair. There are plenty of spouses who have so much going on in their lives (OP is main breadwinner, moved countries, has children) that husband/wife's affair can be ignored in the hope that it will 'blow over' and the whole horrendous upset of divorce/child custody/ moving countries can be avoided. This course of action is also common for couples who don't live overseas. Look at all the 'my boyfriend won't leave his wife' threads...
If you are the main breadwinner working overseas, the work involved in setting up your life there, is not done in 5 minutes. It's not just like asking him to move out and live down the road , seeing the dcs EOW !!
As The OP has moved overseas for her job, it's a fair bet that the visas they have are based on her being in work. If they separate , her DH may lose this visa and have to return to UK. (He may wish to return to UK anyway) As he works from home, he could make a good case for custody of the children. OP could find herself in a position where she has to make decisions such as leaving her job or losing her children.
These are all real, practical consequences of 'knowing ' about an affair..
For many many people both male and female, letting it (an affair) blow itself out is a valid path. Its not 'the mumsnet way ' but I know many many couples for whom this strategy has worked and the marriage has gone on to be long happy and successful. To forgive or not to forgive infidelity is a choice that only you can make OP, there is no right or wrong way.
That said, it's not an easy path to take as the 'not knowing' would drive most people potty. It helps to have a very busy life where the time to obsess over this is minimal - which it sounds like you have.
For my part - having lived the 'ex-pat' life (a long long time ago) I am with the poster who thinks your DH has been flattered by the attractive, bored ex-pat wife, who has little to entertain her day and has set her eyes on your DH (fresh meat ) Women such as this do indeed exist in ex pat communities. It happens because most 'workers' are the men and the women either don't work because of visa restrictions or choose not to because the salary earned by their DH affords them that choice. It isn't long however before daily shopping/gym/golf/ bridge with the same bunch of people becomes very very dull. Other 'diversions' are sought...
I would meet up as a couple , you will soon distinguish 'the type' and fire a few 'warning shots across her bows' whilst spelling out very clearly the standards of honesty, truth and disclosure expected of your DH in this marriage.