Where is this utopia you speak of? Except for MEM and SDF, which have nothing to do with UA, except for the RJs we fly into there. So basically UA is out.
I’ve often wondered how a two pilot household, with a new born, make it work. Tough stuff. Good luck!

My first thought from reading the post was, awesome! Sign me up for Delta and their DTW domicile!
There's are reasons why a particular domicile is both cheap and junior.

there are plenty of very reasonable neighborhoods within driving distance (1.5 hrs) from Newark and DC for United. Same goes for Atlanta and New York at Delta. Philly in Phoenix for American. I’d rather listen to a podcast or a book on tape and drive an extra three hours a week to do two-days instead of four days and get to see my family. Ultimately, whatever floats your boat.

I personally live in a very expensive area in a very small house, spend a lot of time with my family and have inexpensive/free hobbies that I can do year-round because of the weather. But if you like toys and a big house, there are plenty of places that will fit that bill as well :-)

Again, appreciate all the responses! It is the million dollar question for us as a family. We dont have any little ones on the way yet and we are fortunate enough to be on the younger side of things. Right now I have the most flexibility and adjust my schedule to match the other and dont make the most. But i dont care. I remember the days and family events i got to go too. Not the extra paycheck.

Oh man, that's my dream job. Right there.

That’s why I’ve stayed senior on the 756 the last few years out West. For my dynamic I’d leave the house at 5AM to commute to SFO and home the next day at 4pm after doing a BOS or EWR 2 day. Often times I would swap into a one leg to EWR and DH home the next day. I’d either turn and burn same day or just get a good nights rest and be home at 10AM the next morning after deviating home. Many months I’d be home 25 nights a month. Really nice way to stay relevant at home with the wife and little kids.

My experience has been that productive 4 days and 1 days go very senior, but great 2 and 3 days can usually be had much sooner (~50-40% BES) and can give great QOL with a family.

To the original poster, find a place that works for your hobbies, priorities, family network and shoot for a big carrier that has a drivable base. There will be ups and downs, but you’re still probably safer at the big 3, SWA or fedex

Don't forget UPS.

What would be helpful is if the OP would state his & wife's desired places to live, rank ordered. That would help improve any suggestions here.
If the goal is more time at home, don't commute. I want to work as many days in a row as possible as a commuter to reduce my commute. Even short call as a commuter means time away from home vice someone who lives near their domicile can sit at home on short call or at worst drive partway to the airport and sit in a Starbucks. I have to fly to my domicile and sit around the airport during my short calls, or get a hotel if the short call hours are very early or late.

Ok to clear things up,

The simple answer is FedEx, we live approximatly 2 hours from memphis. We have lived in base working for the same airline. He have also been furloughed at the same time. We used that opportunity to move back closer to home and family where we currently are and we now commute to separate companies.

Due to the furlough we are now not on the same career progression as before and are looking at all our options, ideally with the one that gets us to being a lineholder at a LCC or Legacy carrier with the most schedule flexibility. Trying to cast a wide net and looking at retirements and contracts.

Depending on which direction from MEM you live, the best alternatives to FedEx are
Delta
American
UPS
Southwest

United should not be on your list unless you and your wife are willing to pick up and move to one of United's hubs.
Spirit, with DFW, maybe. But I'd stick with the list above and expand from there.