Tell him you want marriage - if he refuses. You could always change your surname to that of your children's and partners by deed poll. What about your home etc, who does that belong to? If everything is in your partner's name then you are bound to feel insecure.
If you tell him how you feel and he refuses to marry you, then you could always play him and his own game. Make a life for yourself and your children, stop doing his cooking, washing, meals etc. Let him be the one that starts to feel insecure. Book yourself a holiday, just you and the two children. All this might work, or the relationship may end, but at least you will know where you stand.