I don’t think it’s bad enough for assault charges. But it could be considered domestic abuse and who really knows? It’s tricky and not straight forward

Intent to push someone is some type of abuse but it could be also explained that you felt threatened by him and tried to get him out of the room. If police was called they might also question domestic disputes of this nature happening with children in the house (unless they were elsewhere) and police might get social services involved.

Right now it’s not an issue since he didn’t call the police and I doubt it’s criminal offense trying to get someone to leave the room. But the whole thing could play out rather badly. One or both of you could be arrested etc if one of you call the police in cases like this. It’s hard to say how law enforcement would perceive such situation