When you slapped in the 98 cd what happens? It should work. In my experience installing my Netgear and Intel NICs with 98se you have to slap in the cd to finish configuring the drivers. That's why your OS is asking for the 98 cd.
What you could do is copy the contents of your two disks and put them into one folder anywhere on your computer which makes sense to you. I have a Data partition which happens to be D: and I stick drivers in a particular folder in my download section of D:
That way when the OS asks for the drivers you can just point it to that particular folder. Another tip is to copy the install files from your OS cd onto your D: using the same idea. That way when the OS asks for your cd you can browse or point it to that particular folder you have it in. Must faster and easier than fishing out your OS cd everytime, especially when you are troubleshooting your comp.
In my experience, the OS is stupid in the way it asks for your OS cd to finishing the driver install. What happened to me is that it asked for the OS cd, I stuck it in, and the OS still wouldn't take it because it was confused. This is with an original 98se cd too. However, when checking the device manager (right click my comp) my NIC had no yellow exclamation mark and it was supposedly working properly (which it certainly wasn't) I then remembered that I had copied the 98se install files onto my comp and then the next time I redid the driver installation (updating drivers through the device manager) I managed to get it working again. Stupid 98se. This may be what is happening with you.
<< Whenever I try to install it it just asks for the Win98SE cd and then installs the wrong driver >>
Or could it be that the driver 98se installed for you was actually crippled? It may look fine but it's not.
Hope this helps.