Here's what you need to do. Buy BidX. Get someone on property to sent you the .asc files for the bidpacks. Download and look at them yourself. Any FDX bubba who uses it can show you how to download bid awards for the last few months and see what guys fly. Look closely at the trips, and the trips junior guys can routinely hold. What makes once guy hold his nose might be attractive to you and vice versa...so I'd get some DATA vice opinions and make your own assessment.
3 kids in the house under 4 sucks....regardless of what you bid. I dont' mean its not a magic time full of love and happiness, but I don't think anyone looks back at those times and says "those were the highlight of my marriage". Kids get sick, puke, crap, and cry more when you are on a trip. I raised 3, but we spread 'em out a bit more. God bless you and the challenges you have, but its also a magic time.
I'll throw out two "outside the box" solutions.
1. Bid HKG. (I'm not kidding). Rent out your VPS house to military bro for 3 year assignment. Get a helper--live in or live out doesn't matter. Bid reserve. Mom gets an extra set of hands, you learn the 76 and fly to some cool places when the phone does ring. (Hint: It doesn't ring much here). Commute to VPS once or twice a month for an 8-9 day reserve period. Fly and blow stuff up. See what you did there? You just lived like you bid an international trip on the 777..but inverted it.
Gone to other side of the world to work, home with fam the rest of the time. FedEx covers your (modest) house, oldest's preschool, and you spoil your wife 3 years. Bid back to MEM/VPS in 3 years before you start paying tuition for kids 2 or 3. One commute per month, less than 10 days. You and wife can have dates in the one of most fascinating cities in the world while helper entertains the kids.
2. Bid for big pay...777. Commute to MEM once a month (via BFM or TLH j/s) and go make money. Take % of those dollars and dedicate to in-house maid service or nanny support back in VPS.
Your issue isn't flying. Your issue is babies in the house. Get some support. Don't make your wife a single mom if you can avoid it.
Here's the gig: Rule 1: No matter what you bid, your wife is going to be overwhelmed at times. Make money, and get her some extra support. THAT is what is going to make her happy. You will make $1000 day year two on the 777. Would you rather stay at home and change diapers and forfeit that money, or would you rather pay someone $100 a day to do that and help and pocket the $900? By the way--even if you are home, you won't "do it right" anyway when you take care of the babies. Pay an expert, and do all you can to turn the baby momma back into your wife/girlfriend. She'll appreciate the support. Rule 2: You will have sex X numbers of time a month with your wife. Would you rather have X/30 or X/18?
If I sound like an ass here with that pragmatism, I'll offer than I've been married to a wife I adore for almost 28 years. I've raised 3 girls..one's a pilot, one is doing well in college, and one is tearing it up here in an international IB school. The key to a happy life is not how many butts you wipe or hours you spend in the kitchen, but but rather making sure your wife feels like you invest in her happiness. I've had this talk with my daughters--instead of spending tens of thousands of dollars on a weeding, how about you have a more modest event (that last a day) and invest in doing some things that will help you marriage down the road. A honeymoon trip is a waste as a newlywed--you'd be happy screwing in motel 6 at that point. After 3-4 years of struggling as you start off on your careers, however, and throwing in a baby or two a mom and dad getaway to Cozumel or Hawaii might be pretty valuable. A little domestic help also can reduce a lot of house tension. You are about to embark on a new career, and there's going to be a lot of stress no matter how wonderful a husband or lovely of a wife you each try to be. Get the tools in place now to reduce that tension.
(Dang...sorry if I went Dr Phil on you here. I've just met so many sad and miserable divorced pilots and I don't want anyone else to join that club...)