What a beautiful story.
I'm sorry for your situation.
It reminds me of a couple that I know that ran into a similar problem about 8 years ago. I'm going to call the couple Ally and Doug. Ally got to a point where she didn't feel she could be with just Doug anymore, but she loved him and they both loved their kids.
Ally found another partner, Mark. Mark is a nice guy, he likes kids, but he doesn't want to raise kids himself, still he gets along with them. Ally and Mark have been together about 4 years and have a close, intimate relationship. Once a week Ally and Mark have an evening together (Friday evening). The following Saturday after the kids go to bed is Ally and Doug's date night together where they still share intimacy. Mark seems content with the relationship because he still gets to see Ally, but he doesn't feel "tied to her" or feel to much obligation. Mark is also entitled to see other people, which he does at some times, but they have an agreement he wears protection.
Doug himself found another partner, Lisa, a fellow parent the couple knew because their children are friends. Doug and Ally both knew Lisa from school functions such as school plays, the PTA and other events. Lisa is also married in a similar situation. Lisa is happy to have Doug as a partner, because she is also married and very active in her kids lives she also isn't interested in giving up her marriage and independence for Doug. All the kids understand the relationships and are comfortable with it. With Lisa, it's easy to find time because they are both already invested in their kids lives and already they are in the same community. Twice a year Ally and Doug go on vacation with their kids. Once a year Lisa and Doug go away together for a long weekend of about 4 days, while Ally watches the kids. Once a year, Ally and Mark go on vacation for about 4 days while Doug watches the kids. They really are a very close family.
It can be hard to find people like Lisa and Mark who are happy with the situation, but they are out there. Please note this is not swinging, it's a hiarchial polyamorous marriage. Doug and Ally both put the kids first, and so does Lisa. The situation is not perfect, problems always arise, but they've been doing this for about 7 years total with different partners, and it works out quite well. It helps that Lisa is already involved in their parent's network.
I also knew another couple, Sandy and Dan, where after 10 years of marriage Sandy realized she was a lesbian, but wanted to stay in the relationship. Sandy found woman partner, who became close friends with her kids and husband. Dan was happy he got to date other women in the arrangement. It worked out pretty well for about another 10 years, then the couple split for unrelated reasons (their kids were grown by this time). Maybe find a local polyamorous group nearby, and set up an OK cupid profile explaining the details .Not everyone is into hierchial polyamory, but there may be more couples like you, and other men who want a loving relationship, value your relationship with your kids, and are happy being in their lives with out the responsibilities/oblications of being a co-parent. If you are comfortable with them having other partners, they will probably be game.
Polyamory does take a lot of work though, and everyone's feelings need to be respected in the process. But it might be worth looking into.
