The Exporter variables @EXPORT and @EXPORT_OK and your exportable $EcoRI should be package globals, so declare them with our or use vars rather than my. You also need a package MySequence; declaration at the top to set up the namespace. [ I missed the initial package declaration before code tags were added. Why do you give the package a different name than the file? That my cause confusion.]

There may be more, but that's what I catch at first reading. Code tags would make it easier to scan.