A mouse will never work well in emulating a joystick. There is (or was) code in Stella to do this, but I may have removed it. They're just too different in terms of output. A joystick can be pushed right, and for as along as it's pushed, an event is generated. For a mouse, you move it right, it generates an event, and then stops. There's no way to get it to emulate a joystick, unless you keep moving it across the screen. Basically, one is an absolute axis device, and the other is relative.
I suggest sticking with games that are programmed for mouse/trackball when using a real mouse. It will never work to your satisfaction when using a mouse to emulate a joystick in a joystick-only game.
I downloaded vjoy last night but didn't try it. Not aware of mouse-to-joy, so will have to look into it. Thank you. I ended up figuring out how to run colntsc.bin (colony7 joystick) with a2600 in MAME, which worked with a mouse, although setting up the command prompts is a pain and the resolution is also much worse with a2600 in MAME than with Stella.
My USB mouse is a Kensington Expert trackball mouse, so it is similar to arcade style, only smoother.
Using the USB trackball mouse to emulate the joystick in MAME is slower than with the trackball hacks in Stella and, as I said, the graphical resolution is much better in Stella. It was faster than using my actual CX80 in joystick mode through the 2600daptor.
Mainly, I wanted to see if I could implement a way to play 2600 games I would like to play with a trackball mouse if there is not a trackball hack. However, as Stephen said, the results are not ideal and more just a novelty than a best way to play.
From what I have learned, I plan to see how my actual CX80 works in Stella through the 2600daptor II using the Atari mouse setting in Stella game properties > controller. I knew there was some difference between the CX80 and CX22, but had forgotten that the CX80 is actually like the Atari mouse. Basically, the root of my problem was that I was thinking of the CX80 as a trak ball rather than an Atari mouse.