simultaneously connecting to two networks separating local Lan to one, and internet to another

Question

I have a computer (call it #1) with two network adaptors. The first network adaptor connects to a private internet via dhcp (giving me an ip address of 192.168.203.212)

The second network adaptor connects to an internal LAN network which provides me with a static ip address (192.168.1.25) and the computers on this internal Lan network have shared drives which I connect to by addresses like \station2\share2 (I could also set this path to \192.168.1.10)

My question is I need computer #1 to be able to make simultaneous internet quires, and also be able to connect to the internal databases on various Lan computers e.g., \station2\share1 , & \station3\share3 etc. Computer #1 is running an Access database program requiring it to query an internet database and then also query data on local Lan shares i.e., (\station2\share2) etc.

I have read that I can set a priority for one adaptor and if that adaptor cannot or dose not know how to route the computer will time out and it may be able to send it out again to the lower priority adaptor but will lead to delays. The data required to run the database requires responses from both networks. And before anyone asks the desired end points required cannot be moved to one network. A Linux programmer said he had heard of a "routing table" that may be able to direct all Lan traffic calls to a specific adaptor but he did not know how to do that.