What connection string to use to connect to network server?
I found a solution. Maybe someone could expand on this, because I don't fully understand it.

When I opened Management Studio as MyMachineName\SQLEXPRESS which I normally do, attached the database there, I couldn't access it through MyMachineName\SQLEXPRESS in the connection string. 

However, when I reopened Managment Studio as MyMachineName, attached the database there, and removed the \SQLEXPRESS from my connection string, I can now access it. 

Problem solved.