I would think it would be easy to have the divorce convo with her since you two have already talked about how the marriage isn't working and things need to change. You can simply tell her that even though you've gone to therapy you are not seeing the changes or effort necessary to make the marriage work, you don't want the status quo and it's best for everyone to amicably part and move on with their life. Tell her that you want a simple divorce for the kids' sake and that if there is a battle during the divorce the only people that ultimately win are the lawyers getting paid (plus it doesn't sound like you have a lot of money to fight over anyway) and that its best for the kids that the divorce go smoothly. Tell her you still want to be an effective co-parent with your kids and that you want to maintain a positive relationship with her after the divorce, but as far as you and her being married that is just no longer going to happen.

Some here (Goggins) will insist you need a lawyer to fight for everything, but it doesn't have to be like that. Work together as mature adults and save yourself a lot of money and aggravation. This will also set you off on the right foot as far as raising/sharing kids go. You're still tied to this woman for a long time.
Actually, IIRC, Goggins had a mediated divorce.. as did I. But our mediator, a retired family court judge, basically told each of us that we would still need lawyers to advise us on matters of law, as that was not the mediator's job. Now, finding a lawyer who "gets" the mediation process, is the trick. I had a top-notch law firm, but my ex's lawyer dropped her over billing issues (not the reason she gave the judge, but that is in fact what it was), so she needed to get her own lawyer. The mediator was able to provide her a list of lawyers who understood the mediation process and whom she could recommend.