You're certainly not annoying anyone but you might be looking at the concern from perhaps one angle when there might be more than one. Here's a possbile reason why.
Windows, be it 98, 2000, xp, whatever, also looks at the stick when you plug it in. It "sees" the controllers plugged in but may not "assign" them to work together until you go into the game controller in windows and tell the program that you want the stick, throttle and rudders working as a team. If you don't do that you may having the trouble you're asking about.
As far as trying to reassign buttons 9 and 10 in AH that is fairly simple. But, remember I told you some buttons are "hard wired" meaning when you plug the stick in you already have them doing a particluar function. You should be able to change just about any assigned function in AH2. To do this you have to go into stick mapping and see what those buttons have already been assigned to do. Then clear and reassign them to a new fuction.
The path to stick mapping from within the game is;
esc key, then under map look at the list and click setup/controls/joystick/stick mapping. That is where you will make the changes.
All stick/thr/rudders are different. For instance, the newer usb CH products have to be "ganged" together in the mapping manager or they will not work correctly in AH.l My old CH stuff is always set due to its ability to keep then stick set even with the computer turned off.
Regarding the other game, I have a buddy who was both an F4 and F16 Fighter Pilot Instructor, ala Red Flag and he asked me to run it with him. To make a long story short, when I loaded the game and fired it up, my pedals worked perfectly without my having to do anything.
Any trainer you run across in the Training Arena (TA) can help you through the AH2 stick setup. Drop on by the TA.
Also, don't hesitate to ask any questions here. This is what we are here to do.

Suggestion: if you are looking for more info on other games you may want to look around for forums on them as they deal with their issues daily just as do we here for AH2.
Hope this helps.