My kids were 7 and 5 when BD happened. Due to moving around a lot and my employment not being as concrete and lucrative as exW, I was able to cushion those moves by taking time off work to be with the kids and avoid daycare costs. So, I've had a pretty involved relationship with the kids since the very beginning. I did the stay-at-home-dad thing for a bit and it gave me all the skills to take full-time care of my kids. Now that they're older, it's easier with some things because they are getting more independent.
But as I mentioned, even though I was 'able' to perform all the tasks etc around childcare, I was still not the greatest parent emotionally and mentally with them. I was short with them often and my parenting could've used a lot of improvement. As I took care of my own emotional issues, it had a compounding effect on m parenting in a positive way. I had also mentioned books by Robert W. Greene and Shefali Tsabary really helped me in understanding my role as a parent and also how to engage with my children. I had to unlearn a lot of subconscious parenting things that I was carrying over from my own crappy childhood. This wasn't easy - I went to task on myself and was brutal with myself about it. I had to because the status of my well-being was directly impacting the well-being of my kids. With exW being all WW and entitled etc, I knew that I had to be the solid parent in the equation to create stability, love, and safety in the home for the kids.
I initially did that by generally suppressing my own emotions, but that was just a stop gap and instinctual response. Even though I was making some gains in other areas of my life, the emotional stopgap was holding me back. Life has a way to put your pain upfront and gnaw at you until you break. That happened over a year ago through a very dumb incident that brought grief to my kids. It happened in a public place and I held my emotions in but it was killing me inside to see them be upset. That night, after putting them to bed, I broke down and released what I was holding back. It took a good few days to get it all out, and then a few weeks to parse through it. That was an important breakthrough and I got on the right path to improve my emotional health. That's exactly when Shefali's book helped me and I was able to cultivate my identity as a parent and what I valued with my kids. But, until you get yourself right, you're going to be terrified of being a single parent. The tasks are easy - you can learn them over time and you'll get that. But creating emotional safety and security for your kids is the more paramount issue, which you can do when you get on the path of developing emotional fitness.
Taking a U-turn in my response, you are trying to create connection with your W through vulnerability, and she is rejecting you. Read Brene Brown's book Daring Greatly. Game changer. What you need to understand right now is that your W is not interested in building a connection with you. you can try whatever you want, it's just not going to work. Also, your vulnerability is making you look weak in her eyes. This is the crazy truth about vulnerability I have learned - women want men to be vulnerable, but when men truly are, women lose respect and are disgusted by it. So, the important thing here is to understand how to dose the vulnerability. And that works with someone who is open and receptive to you. Your W isn't right now.
I would highly suggest that you work on your emotional health out of sight from her. Don't become a stoic stone-cold dude, but be more collected and calm even when it's killing you inside. I know that feeling and it was hard to do, but if you want to command her respect, that is one of the things you need to do. As you improve your emotional health, it'll become easier for sure. The LL's as I see right now are inconsequential because she is not open. And you shouldn't have to sacrifice your LL to stay in the M.
I know you want to save the M right now and it's all your focus, but take some time to think what you want in a partner and if she actually meets what you want? What would she need to do to have your partnership? It's all cloudy right now, but ask the right questions to yourself and start formulating honest answers.
