My headcanon was Neal was convince to leave by August with some connection to the big bad. That pretty much if he stayed with Emma the bad thing that would happen would be Emma might die. We know he didn’t know of Henry. So basically it would be that staying together means Emma would be in danger. I believe MRJ and Adam and Eddy discuss several options why Neal shouldn’t have to leave. So I assume what ever they decided it would be big.
As for the jail incident I think either August or the Darlings called the cops. I think Neal was trying to do some spying on Emma and contact August. August then later told him she went to jail. Neal figure that Emma went to jail because she got caught as accessory. Thus Neal is basically blaming himself for one leaving Emma and two getting her involved with his crime. If Emma didn’t help steal the watches she would be free and find.
"I will be kind but I will speak my mind."