TALK to your wife BEFORE you do anything else. Do not bring the elders into your marriage. You may get what you want in the short term, by invoking JW headship rules on your wife, but I guarantee you undermine productive communication and trust with her.
You need re-affirm your love and care for her. Ask her what she needs. Ask her what she wants. Then tell her what you need. Tell her what you want. (And I'm not talking about "don't touch my man cave stuff" or I bought you a new mattress in exchange for keeping kids out of bed") Dig deep and lay out your heart for her...Examples: "I want to spend more time as a family with you and the kids", "I need us to spend more time with my friends and relatives", "I miss you when you are away", "I want and need to spend more intimate time with you", "I want to see a marriage counselor to help us get closer and communicate better." If she loves you, hearing that you love her and want to be with her with let her know you have forgiven her cheating and would like to move forward. It's all about time ...you have to make time for each other and for those kids. Make sure you see her as a woman and a valuable partner, not a nanny and housekeeper. I would not approach the pioneer thing, just build your marriage and she will crave time with you, which will exclude time spent in other activities.
P.S. About the man cave...if you are spending your free time in there playing video games and what not, instead of time with wife and kiddos, then of course she'll choose JW activities over home.