Either let him figure out how to balance his life on his own....or with you by trial and error. But not by using "marriage" as his quick fix hoping that this will "cure" his ails.
You really can't blame him, its not an easy fence to walk, nor for his Ex.
He will still have strings attached to his Ex and kids....for life and monetarily. His Ex doesn't "have" to change...as far as she sees it...and perhaps she is a little "possessive" over him and/or jealous. Well, that's natural...she probably does not want to see her children neglected once their Daddy has a "new life" without them. At least his Ex still includes him in her children's lives. Many don't. So, there is that side to it too.
Like it or not... your are lucky to know a man who CARES about his kids and wants to be a part of their lives, even if he is no longer with their Mother.
Now, you need to decide what to do with him. Perhaps your boyfriend and his Ex are STILL transitioning their lives separately....and while still being present and a part of their children's lives. So, they still have kinks to work out.
If he truly cannot balance his own life, in conjunction with his Ex, separately....then you will have the Ex in your life too...like it or not. Which is sad for him, because then he can never really live his life or have happiness. But at least he is a good willing Dad to his kids, and not an absent father.
Do you want to be a part of that...or not? But, make sure that as admirable as he is for being a Dad to his children....that you are not being taken for granted either. It may take some time, in working this out, if you stay with him. Or, perhaps you both can go to couples counseling to investigate this further and get ideas from a professional... what would change if you both got married? And, maybe he can learn coping skills and how to set boundaries with his Ex. Sometimes, men, even with the best of intentions, really don't "know" how to set boundaries...and being a good Dad at the same time. You are lucky he loves his kids, and wants to be with you. Try couples counseling, it might shine a new light into the picture.
BUT, are you BOTH willing to go this extra step, for your relationship? Are you together really, because you want to, love each other, enjoy each other, complement each other....or because it is a habit and don't know what else to do? Have a heart to heart talk... what is his and your, level of commitment to this... then, decide on a "solution" and a plan.
All the best,
~Susan