OP, I am sorry to read your update.
I also work in a field that requires a lot of travel. I have moved up the chain so my travel is much more limited, only a few times per year and most of it is local. But, my direct reports are on the road Monday-Thurs/Fri and sometimes leave on Sundays.
The single young men and women usually do really well in the job. Young couples with no kids do ok sometimes- better when both are in traveling jobs.
There are some couples and families who do well when one spouse travels for work; the other is usually an At-Home parent. For whatever reason, they are both in complete agreement and support each other.
There are many, many couples and families who want to make it work, but it doesn't work. The unit falls apart. The at-home and the kids are the integrated family. The worker is an outsider, a benevolent supporter, and that's about it.
Not to be Captain Obvious, but it is clearly not working for your family. I agree with @lifeistooshort
, you started off the thread saying that your marriage was awesome except for it being sexless. Many posters pointed out that your wife is drowning. It is not an awesome marriage for her. You are the benevolent supporter. She doesn't need you during the week- she might be barely treading water but she's doing it on her own-and she's not all that interested in you when you're home.
I would be surprised at this point if she agreed to having you home. It's probably more emotionally comfortable for her when you're away. I still think you need to talk with her, talk some more, until she agrees to it. Your marriage is at very high risk, you both are vulnerable to making very bad decisions due to unmet needs and 80%+ of your time is spent apart.
If you two get divorced, not much changes for her. She still will be the one doing everything. She is probably not very afraid of being a single parent, she is one most of the time as is.
You will not be able to get much custody if you are on the road Mon-Thurs, you'll be paying a lot of child support. Yes, she'll have to get a job, and put the kids in child care. Guess what- her life will probably be a lot easier, actually. She'll even get some weekends totally kid-free.
If you get divorced and hope to see your kids more than every other weekend, you will need to quit your job so that you are available during the week.
It would make more sense for you to quit the job now. You are going to take a financial hit one way or the other, better to do it now and take the chance to save your marriage.
I don't think either of you are to blame. Try not to take things personally. The traveling work is a situation that your family tried, but it didn't work. It doesn't work for the majority of people. Just see it for what it is, adjust accordingly before things are irreparable.