He lied to you. He stole from you. He told more lies to cover up his lies.
This is the man you know.
Checking out of rehab early is a huge red flag.
Suggesting that you are a trigger for relapse sounds like rationalization to do so.
Sounds more like you have taken on the job of being his warden instead of his GF. Is this what you want out of a relationship?
Either you accept him as is/where is or let go. Anything in between is hell.