Your husband is doing his part to heal the relationship. He admitted that being in touch with the woman was an ego boost. He’s leaving his phone open to you. Your focus now needs to be on yourself.
It sounds to me that your relationship had a difficult beginning. You moved in together and became parents before you were ready. He kept one foot out of your relationship for 4 years (!), being unwilling or unable to commit to a marriage. I’m guessing that the kids were an important “glue” during those years but not enough to make him stop thinking about other women.
Although he eventually did commit and hasn’t cheated since, you haven’t forgotten or entirely forgiven those early years. It’s not unusual. There’s an old saying: “Once burned, twice shy.” Once trust is broken, there is often a residual guardedness in the person who was betrayed.
Your husband’s flirtation picked at an old scab. One thing he can do to help you move forward, since his constant phone use is triggering for you, is change his phone habits to be more family-friendly. There is no reason short of a major catastrophe to be on the phone during family movie night. He should be able to confine business to business hours. Staying connected with extended family should include you and the kids.
Your side of it is to decide if this incident undoes all the good that has happened for the last 11 years. If it doesn’t and the marriage is worth preserving; If you really think this connection with the other woman was out of character and an early midlife crisis, then your challenge is to find a way to truly forgive him. It’s not easy. You’ve been hurt – again. That’s something you both need to understand as you move forward.
If you can’t find a way to stop the overthinking, I do recommend that the two of you see a couples therapist for some help managing the aftershocks of both the early years of your marriage and this latest lapse. If your husband won’t go, then go yourself. But I hope he will. Some honest conversations in the safety of therapy could help you clear the air once and for all and establish a commitment and trust that will hold.
I wish you well.