The computer is using DF1 Full Duplex protocol over RS-232 to communicate with the DF1/DH485 converter.
The problem is that DF1 Full Duplex is a point-to-point protocol; there is no way to determine which PC would be able to transmit (and indeed, which would receive) data through a serial splitter.
I can think of a handful of solutions for this problem:
1. Install RSLinx Gateway on the SCADA PC and allow it to be the route through which you connect to this DH485 network.
2. Install a second PC with its own RS232/DH485 or even USB/DH485 interface, along with RSLinx Gateway, to be the bridge between a TCP/IP network (almost certainly a VPN, not the Internet itself) and the DH485 network.
3. Use a standalone Ethernet/DH485 gateway from EquusTek (aka DataLink aka protocolconverter.com).
4. Use an Allen-Bradley 1756-series chassis with a 1756-ENBT and a 1756-DH485 module.