Sqlite is file-based only. There is no way to talk to it over TCP/IP.
Like an Access database file, you have to have the database file in a network shared folder. The path is usually going to be a UNC path, like "\\server\sharename\folderpath\databasefile".
The problem is the connection string you built isn't a connection string. It's a partial string. You have this:
DataSource = @"\\\\" + txtipaddress.Text + @"\qscanDBAttacheds\test.s3db;Version=3;New=False;Compress=True;"
The "DataSource" part has to be part of the string you build. You don't have that. You need this:
string connString = @"Data Source=\\" + txtipaddress.Text + @"\qscanDBAttacheds\test.s3db;Version=3;New=False;Compress=True;"