Thing is we can sit here and come up with all sorts of reasons why he keeps his family secret. But to what end ? How would imagining all sorts improve your life day to day ? I strongly suspect it wouldn't help.
It's a cliché and it's well worn but the adage You can't change someone else, you can only change yourself applies in buckets here.
For 6 years this man (who I don't doubt for one minute you love & care for) has not shared details about his family with you, has not taken you to meet his family, doesn't defend you at all, let alone to the hilt, when his family are rude about you and about your DD. He will not discuss details for a wedding or set up joint accounts.
He hasn't changed his position in 6 years. You've spoken about this but he continues as before. I'm sorry about as a stranger looking in from outside of your situation, this is not a long term, loving, supportive relationship. You are clearly realise this at some level as you are unhappy and have asked a bunch of strangers, most of whom live half a world away from you, for help. I think everyone who has replied to you has said pretty much the same thing - this relationship is not going where you want it to go.
The choice is up to you - you can continue to live on a knife edge, not knowing how he feels about you really, being unhappy about lack of marriage, etc etc. Or you can take control - work out a plan of how to separate and build another life.
You don't have to leave today, but start making and actioning plans. Please