Connecting to SQL Server on different Network

I am still a sophomore computer Engineering majoring student. So please bare with me if I have questions that might sound stupid.
Scenario: 4 Pc's connected to SQL database through same network perfectly
3 Other Pc's on a different network that I am trying to connect to the database on the other network

So: Network 1: 4 pc's where one of them is the server - connected perfectly

3 other pc's connected to a different network that I want to hook up to the same SQL Server Instance 

I got over the problem with a VPN but it was very slow.
This is for my Father's clinics so servers must be running fast.

Any suggestions :( ?? 

Apologies for poor English