If you can't export and input one row sucessfully, then your problem with trying to export/import a large data set seems besides the point.
Any ways, your problem with a large query can only be fixed to my knowledge by adding a new setting to the mysql my.cnf file, which would have to be done by your hosting company.
The setting is: set-variable=max_allowed_packet=15m
In this example, I've increased the max_allowed_packet to be 15 megabytes in size. This would need to be roughly the size of whatever your insert statement from your export is.