My guess is multiple reasons. The one I feel might be closest is that EG and JH didnt want JO to know that there were 4 people living in a single bedroom apartment. Next would be that maybe their house was not well kept (IE: filthy) and they didnt want JO to see that.
In my own head, I argued with myself about how neither of those reasons make sense because why would they allow EGs boys' father to come to the house? Granted, EG was not allowed to drive with her sons in the car, so options were limited as far as that goes.
So, how was JO going to the house different from her EX? The only reason I could come up with was that it didnt matter if EGs ex saw their living arrangements because HIS kids were not living there nor sleeping over there, so they dont need to hide it from him, however, JOs child lived there 24/7. So, beyond the fact that the space was too small, what were they trying to hide from JO but didnt care if EGs ex saw? All these freaking initials! Hope I kept them all straight!
Also, I seem to recall that the paperwork the ex filed stated that EG was not allowed to drive their boys without another licensed driver in the vehicle. There has been alot of talk about how she wasnt allowed to drive LH or MH around, but I dont believe that court order applied to them, only to EGs boys. He could not have something added onto a court order for children that are not his. JH or JO would have had to have to request that for EG not to be able to drive LH around. She didnt have an actual restricted license, if I am understanding it correctly, it is just part of her family-court ordered parenting plan. My understanding is if she got caught driving with the boys in the car, and it got back to EGs ex, he could petition the court again.... kinda along the same lines as the "if u do drugs, u are choosing not to parent thing", sort of.
GAHHHHH that was longer than I intended!