I'm going to tag onto this post as it is constructive and in a positive way.
Another couple of things to remember (and this was also mentioned) is that your children are looking to you for social behavior and while you are aware of your flaws (which is good!) as they grow into adolescence (and with a 10 year old that is closer than you think) they are VERY aware of them. Daughters and sons want attention from their fathers and these years right now are IT. Meaning as they hit the teens and begin to bond with peer groups and want more privacy for teenage thoughts and dreams, it gets more difficult to express the emotions bubbling beneath the surface in positive ways. For both of you. While my spouse was an engaged father with our children when they were little--swapping off reading aloud, bath time, etc as they got older, we had a conversation about those nearing teen years and how more than ever, this was a good time for Dad to really step up and be there as a person of character for them. Forget the patriarchal society that we live in (if I hear alpha male one more time, my rolling eyes will fall out of my head) and just going with things like 'how does one resolves disputes, how does one learn about compromising, or forgiveness, or walking away from a bad situation or when to stand one's ground.' None of these things have to be about being male, per se, but how to be a human being. How it's okay to cry, to be weak, to ask for help, to confess to feeling overwhelmed or lost or angry. How some of these can be used against one (revealing too much information to untrustworthy acquaintances) and how to navigate that in relationships--personal, professional, and just out and about in the world.
One of our children is pretty introverted. Like the OP, my spouse is quite drained after work but something that helped us was me commandeering the evening meal prep so that the two of them could take a walk. It wasn't a terribly long walk, but five to ten minutes into that walk and the words would just spill out of him. To this day, they still take a walk together whenever this (now adult) returns home and you wouldn't think such a small somewhat uncool thing would matter but it did and it does.