The closest fbg situation to yours here was Bogart's. I'd like to hear his thoughts on this if it hasn't already happened.
I believe bogart has been divorced for a few years now.
Well I mean that he might have some insight after pulling the trigger, he had a non responsive wife, and kids.
I went through this a few years back. We had our kid just over a year into the marriage, and post-partum depression and weight gain followed. Health issues for mom and kid led to some form of anxiety disorder for mom, which combined with everything else took sex off the table from her perspective. She went to therapy, we went to therapy, we talked about it a lot, went to a different therapist - no change. Sex and intimacy just weren't an option for her.
Eventually, I think after our third different couples therapist, she told me to go ahead and fulfill my needs elsewhere - she just didn't want to know about it and it couldn't be anywhere near our social circle. Ashleymadison.com actually worked for me and I hooked up a couple of times, but she then checked my phone and freaked out and said that was now off the table. Back to yet another couples therapist, still no change. By this point, obviously, divorce was on my mind. I went back to ashleymadison and resumed my activities, was just more careful. While the strange was fun (damn there are some freaks out there!), I never felt good about it and was always conflicted, not sleeping well, etc. Unless it was a family event, our social lives became completely separate. She ate dinner sitting in bed every night, I ate in front of the tv or with the kid. We hardly spoke, living basically as roommates taking turns parenting.
The conflict for me was similar to what OP is talking about here - both financial considerations as well as wanting to be a good parent and "stay in it for the kid" vs. modeling a horrible relationship for my child. I didn't want my child to think that's all they should expect from a marriage, and that really was what helped push me in the direction of a divorce. The financial part did suck - even though we avoided court and managed to decide everything via a mediator, I was still hit with alimony and child support, even with 50% custody.
I'm not gonna lie - the first couple of years kinda sucked. Due to the support payments I was stuck in a small apartment for almost three years, while my ex stayed in our house for 9 months and then ended up shacking up with a "friend" she'd had for some time in a nice house. And more importantly it was really hard on the kid. I'm a super involved dad, get to work from home, volunteer in school, coach sports, etc. So everything that my child was struggling with was right in front of me. A lot of crying at night, "why can't you just get back together?" - all of the terrible and heartbreaking things you would expect, quite frankly.
But over time it's gotten better. The ex is now married to that "friend", and seems to be much better. I've been with and lived with my lady for a few years now, and she's a much better fit for me and I'm so much happier - and a few years in we still have sex all the time! The ex and I mostly get along (and now that she's married no more alimony!), and while there are still tough issues that come up on occasion we've been able to work through it. There is no doubt that this has all had an impact on my child, and a long term one. But I think there would have been other issues had we stayed together. There really is no way to know for sure, but I'm confident that by maintaining my involvement and relationship that my child will end up fine.
I have thought about whether we could have worked it out, and I suppose it may have been possible. But I think the more likely outcome was that we would have spent another 10-15 years in a miserable marriage before finally getting divorced anyway when the child was grown, which is just way too much of what little time we have on this earth to give up.