On a more personal note....When my parents were going through some crap in their marriage, i (an avid gamer) really enjoyed when we would play games together as a family, even if they were competitive or not. My mom, who never plays games, even played, and had fun.
So, basically what i am saying, i'd advise you to spend time with your kid, no matter the game you guys are playing. It doesn't have to be a military shooter for a kid to have fun with their parents/siblings. Just be involved in their lives.
I won't tell you what games to play with them, but whichever you do, just spend time, and i think it will work out for the best. I miss playing games with my parents.