There are no trust issues. None what so ever
This is a tactic which is unassailable as far as he's concerned. Whatever you do (including being locked in a room for weeks on end) won't make a difference to his "trust" in you.
This technique is purely used to ram home that you are worthless, not good enough and will have to keep striving harder and harder to "win" his approval.
On no occasion, not even if you were to kill a rabid bear with your bare hands to save his arse from certain death would he ever accept that you love him enough, or that you can be trusted with his own life.
This is because he hates himself and doesn't trust himself, he is an emotional black hole. Everything you pour in will be consumed yet more and more demanded.
When your efforts (and you've only been with him barely enough for them to start to show) are no longer enough he will hit you, kick you and beat you. He will tear you to shreds in front of your child.
He will hurt your child to hurt you.
Because they all do. To an abuser. This is their script.
You don't love him. You want to be loved, but don't love yourself enough to demand and expect love in return. This is probably as a result of your upbringing.
You can change this. It's hard work, but it's worth it. You are worth it and your child is worth it.
If you don't leave this man, your Dc will go on and repeat this relationship in their own life.