What would cause newly restored SQL Databases to show tables, but display an 'Invalid Object' error when trying to view table data?
It sounds like the objects are still there but are owned by the schema nurse.  So for example instead of dbo.Table1 it would be nurse.Table1.

Your users aren't see the tables because they are not including the schema part of the name.  If the schema is not included

SELECT * FROM Table1


Then the schema used is the default schema from the database principal (user).  In this case, as you said, it's dbo which is the norm.  An easy way to check this would be to do the following:

SELECT * FROM INFORMATION_SCHEMA.TABLES WHERE TABLE_NAME = 'yourtablename'


If the TABLE_SCHEMA value is nurse then that's your problem.  Try changing the default_schema of your principals like this:

alter user [username] with default_schema = [nurse];


Also you could query the tables by including the two part name:

SELECT * FROM nurse.Table1