I will leave out the DEN-NYC specifics as I have no idea. As to commuting to work by plane, I have done it 10 out of the last 13 years, with the last 7 years being continuous.

You: This kind of travel is not for everybody. Don't get stressed and take it all in stride. NEVER check a bag unless it is only dirty clothes or things you can do without for a few days. If you insist on pushing the carry-on limits, then make sure you are first to board please! Nothing worse than the commuter who arrives with three bags and then complains about no bin space. Use Skype or some other videophone/ip service to stay in touch. The added video makes a difference. Sleep on the plane if you can. Do not make the flight part of your work day. It will only add to your stress.

Wife: My wife and I were dating while I was on the road, got married and had kids, all while I was commuting weekly. This is an important difference. Not all wives can accept the "being alone" factor. For many, they feel that they are a single mom. If you can, set up contracts with various electricians, plumbers, etc, so that they will take care of your needs. This will permit you to not have to tell your wife to ring the plumber/electrician to sort something out. Do not think you can have it wait until you get home. Your wife will not appreciate this after a while and it will only add to her feelings of being alone.

Kids: This depends on the ages. I have a toddler and a moody teenage girl The toddler likes the 2 minute conversations using Skype video calls. She knows Daddy comes home on Fridays in a plane (and points at the sky on Fridays every time she hears one) and definitely knows who her Daddy is. I took over all child duties (except feedings) on weekends. This gave my wife an appreciated break and enforced the bonds with my child. As for the teen, I always ask her about her day (even though I will only get a "fine" out of her) and sometimes help her with her homework on Skype. The screen sharing feature and the cam make this work very well in fact.

Do not use miles for commute upgrades. Save them for the vacations with the wife and/or family. Same for hotel points. These "perks" of the job can go a long way with the wife when used for a weekend in Vegas or 4 days in Mexico or the Carib.

Find what works for you AND what works for your family. Each situation is different. My wife will drive me to the airport and pick me up to save the €50-€70 in parking. We then spend this on a dinner when I am home. Try different things and settle on what you agree works for the family and you.