how she met my son and spent time with him and how she loved being with him, how she will love our kids as her own and make sure he is happy and balanced...
This is just plain revolting. I wonder if they had told your son to keep it a secret.
As you may recall, I found out about my XW's PA from my kids. My L said that I had a great chance to have full custody because of her exposing the children to her affair. But I ultimately decided on what is best for the kids - 50/50 time with each parent. It seems to be working out well.
There exists the possibility that your STBXH will live with her permanently and your kids will live there part time also. I am not sure there is much you could do legally to prevent it. You will need to learn to bite your tongue of what you would like to say to the kids about their father and his girlfriend.
Also, bear in mind that sometime in the future, you may meet someone nice that the kids like also. Your STBXH will also be faced with the idea that another man will be in the kids lives.
I know you say that you need to know all the details of the betrayal, but at some point you have to stop snooping for your own good. Use the information you have now for your advantage in legal proceedings, but as you have said before, Greek divorce law is not fair for women. Hopefully, some legally fair financial justice will come from this.