MAME should/might see the controls as they are. Other games/emulators can sometimes have capture functions that you can use. However, nothing is perfect, so to bridge the gap...
I'm using UJR, which is an autohotkey-based joystick remapper that works in conjunction with Vjoy to create a virtual wheel in this case and feed it inputs from physical sticks and wheels. However, UJR doesn't handle force-feedback, and may only take inputs from sticks and wheels. The project was abandonned some time back.
I think the creator went on to make the UCR project. This seems more flexible in terms of what you can do, because you can have keyboard inputs feed to joysticks, etc. And i think it might have force-feedback.
Whichever one you use, it will be a pain to set up. You have to be pretty patient and work everything out, minus a few tutorial bits on youtube. You have to use the Vjoy feeder app in programs like teknoparrot, or anything that sees your real wheel as well as the virtual one. The advantages are you can remap everything, and in UJR you can use profiles linked to games via their autohotkey windowclass - you will probably want to get autohotkey as well. These profiles can change the mappings of course, but also per-game sensitivity, pedal options, et al.
You could also take a look at Boomslangz universal FFB plugin. I'm not really sure what it does but I'm about to dive in myself as someone gave me an old Logitech force GT and i'm going to see about FFB in OR2 and TP.