A rule of thumb is, if you have an Access app that does anything beyond simple data entry - use SQL Server, Oracle or something similar.
Here is a couple of things you could do:
1. If both DBs are on a local servers, you could link both of them to a shared database in SQL Server. You can have a query run in on Access table which would populate SQL Server table. You could have another one retrieve the data from the same table.
2. If both DBs are on local servers, you could try creating a table in your main DB (the one you're reading from) to contain any required data and then simply link it in to the other DB. So once you update one, the other has your data.
3. Create a query in your main DB (where you're reading data from) to select your data and then export it in some sort of format (XLS?) Then simply send it over some medium (depends on data sensitivity) and import.