I have no idea if he's ever telling me the truth or not, and then he gets pissed when I act like I don't believe him.
If you practice detachment from his addiction, you will feel better.
I learned I couldn't trust my son's father to tell me the truth about his "recovery", so I stopped asking. You have so much to deal with - your daughter your house. Let him deal with his addiction on his own. Focus on what YOU need to do to ensure YOUR health and the safety of your daughter.
Try saying the serenity prayer - codie version. It brings me peace.
Grant me the serenity to accept the people I cannot change, the courage to change the person I can, and the wisdom to know it's me.
Boundaries help too.
A boundary I might set in your situation would be:
I value the truth. Since I cannot trust what you tell me about your recovery, I will no longer ask you questions about it.