A DataSet object was specifically created to "collect" and "manage" multiple tables, and work in a disconnected state.  You can even define foreign keys into the DataSet so that if a record is deleted from a table, it's corresponding records in the other table is deleted also.   I would collect your data into ...

  Hmmm.  Your DataSet is not on a page -- it's in your app.  The DataGrid is only a means of displaying the data.   So if these two pages call the same codebehind page, they already share the input data. If you have a different setup then you'd need to provide additional details about where the data is located ...

One solution would be to bind to a DataView rather than a DataSet.  DataViews can be sorted (without a query call)  look into the documentation for DataView and SortFilter. hope this helps.