Do I have any eviction rights as a hotel resident?

Unless there is a contract that you signed and agreed to leave on 48 hours notice, there is no basis for the manager to remove you.  Is there a lease in place?  Or is this living arrangement month to month?  If there is no lease, or 48 hour requirement that you must leave at the motel's request, the manager may make you leave at the end of the month.  The fact that you have a 5 year old child does not protect you from having to move out.  If you fail to move out, the manager may have to file an eviction action.  this may buy you a month or two based on the time it will take the manager to file the proper court document.  I suggest that you find an alternative place to live soon.