Hi op reading your thread I could feel every emotion you felt and are feeling because I have been there and it basically played out exactly the same as your situation.
My partner of ten years done the exact same thing to me. We had one 3 year old and I was pregnant at the time aswell. This was 13 years ago .
Youl go through every emotion out there over the next few days and weeks . Remember tho that they are only sorry that they got caught out . And I do believe what you said about for him to go shopping with her there are more feelings involved.
When a man comes face to face with losing his family or more importantly home comforts he will cut all contact with the other women but it's for how long . Women get more attached than men and she's likely not to end it that easy .
All I wanted was my family back so I stupidly took him back . He was brilliant for a few months . But I suffered so bad . Was paranoid everytime he went out or was on his phone . I would cause arguments and being the affair up all the time . I hated my self . I convinced my self I wasn't good enough , pretty enough ect and that's why he went looking for something else
All them years of feeling the way I did ruined me . I now suffer with awful anxiety because of it . And ruined a relationship after my ex because of what happened.
I just want you to know that what he has done has nothing at all to do with you . If it's in a man it's in them . No matter how beautiful and kind his wife is.
Only you can decide what to do but remember don't ever feel guilty if you chose to end it for good because he's the one who broke your family up not you . They usually go from severely apologetic to when it doesn't go as they plan and you go back to somone you don't recognise and they start blaming you .
Be kind on your self and I know every second of the day is hell for you but you have your beautiful children with you and that's all they need ❤️