You can use system functionality "Bind data" for such purposes. You need to choose the package you want to export. Click on "Data" tab in the configuration and add a new data file. There you choose "Translation" object and columns, data from which should be exported. You can also click on "Display data" button on the right part of the data binding modal window, so to see which exactly data will be added.
Afterwards, as yoo export and install package on other instance, the data will be installed along with the package and the translation object will be filled with new translation in database.
If you decide to update existing data, please set "Force update" tick in the left part of data binding modal window, where all settings are.
