Yup, keep the laptop.
Here's what happened to me.
During one of our breakups, I demanded that my ex go to AA for 6 months, and get his financials back in order, get his life back on track, before I would eve consider a relationship with him. I wanted to go NC with him. Call me when you get your six month chip. I was very strong about this... but he kept pushing, and pushing, and pushing. Eventually he wore me down, and next thing you know I was moving to another state with him. (this was when I thought no contact didn't include reading his emails, as long as I didn't respond it was okay right? wrong! that's what got me)
Please don't do what I did. Watch your contact with him. They have such a great way of determining what needs to be said to get what they want, even when they aren't actively drinking. Give them an inch and they take a mile. Incredibly selfish. He doesn't care that you are asking for space and time, for yourself and your daughter. I begged my ex to give me time for me, and please leave me alone for a little bit, that it would really help me to get some perspective. He would have none of it. The gifts started, the reminders of happy times, the sweet emails. All he cared about is what he wanted, what would work best for him, and he wanted it immediately. He wouldn't stop until he convinced me. As soon as he saw that I was faltering, he really went in for the kill. Every single conversation hid another manipulation, another request, another "please, I really get it now" or "we can do this".
Within 2 months he was drinking and smoking pot again.
Just be careful.