toby You may be right. However DP has many female friends that he has been out for drinks with, worked with away on tour etc. and it has never bothered me. It's THIS woman and the fact he's been keeping secrets
Yes, this is different.
He is already emotionally attached to her.
He wants to be with this woman, he calls or emails whenever he can, he thinks about her all the time. He even contacted her immediately after you told him you were uncomfortable with it.
He has changed his password, he keeps his phone close which is a change of behaviour, he lied about his plans, he could not answer when you questioned him.
He is spending a lot of time thinking of ways to meet up with her and thinking up a feasible cover story. He is not very good at quick thinking when caught on the hop though.
When you asked about going for a bike ride, his response wasn't well thought out and made you suspicious. When you told him outright all he could manage was a strangled "sorry".
He is like a child caught with his hand in the cookie jar. His responses tell you all you need to know. He is smitten with her.
You need a proper, serious talk with him and for him to explain his actions and motivations. Don't let him avoid this. Book a babysitter if necessary and go to a hotel room. Look him straight in the eye and tell him you will wait as long as it takes for him to be honest with you.
If you are not ready to hear his confession (or cope with his ongoing lies) then just tell him that this relationship is making you unhappy, it is eroding the trust and respect you have for him and it has to stop. Completely. No music lessons, no emails, no contact whatsoever, including the children.
I doubt that will make you regain your trust but at least it will nip the relationship in the bud.
Now that he knows you are on to him, he will be more secretive btw. This won't just go away on its own.