Either jurisdiction, military or civilian, could investigate at this point.
If there was no intentional physical contact between you and you child, then it is unlikely the military or civilian will charge you with assaulting your child. Additionally, if your mother did not file a complaint, it is unlikely either will charge you with assaulting your mother.
In terms of CPS, of this was a one time incident, and was ancillary to a fight with your mother, they probably will close the report after investigating. However, to ensure that this doesn't happen again, and that CPS does not recommend removal of your child, I'd advise you have your mother move out.
CPS could see her presence as an ongoing threat of violence and remove your child. Additionally, if one child was removed, yes, they could do the same with a future child.
Both of these are unlikely, but are a possibility