Small Rage:
I wanted to play some games today, as it's probably the last day I'll be able to for a week.
-snip-
Sounds like these people are used to pushing you around and enjoy the feeling of superiority they get from being able to force you to do what they want. Maybe not consciously, but it's there.
Any kind of schedule for guaranteed blocks of time for each person is just going to screw you over: you will end up getting shafted as other people nudge into your time (especially your Mom's "Oh I just need to use it for a few minutes dear") and/or the schedule will get reinterpreted as "this is all the time Cmega3 gets on the computer all day, possibly including homework time" which is bullshit.
Ideally for you, you want as much time as possible.
It sounds like your family dynamics wouldn't allow for earnest talks with your mom on this issue. So you need to be underhanded to get what you want.
Specifically announce to the sister, so that the mom can hear, "Hey I'm going out of the house, if you want the computer you better use it now!" And when you return, find the sister and say "Hey did you get a chance to use the computer during the three hours we were out?" That way Mom will be less likely to side with her. It's clear that the sister had an opportunity and failed to take it. The next three hours are yours, mate.
I wouldn't go so far as taking a necessary cable so that the computer won't work, because if discovered, again, your power position is sub-optimal and you'd take heat for it. Similarly, changing the account password so nobody else can use the computer, and creating an admin account that only shows up in Safe Mode so you know you'll always be able to get in, would be overstepping your bounds. Editing certain files in the programs your sister likes to use, so that they no longer run and she has no reason to want to use the computer, is also problematic (although you could very well get away with it).
Then again, are you really objectively looking at how the situation works most of the time? Do you find that you get your way over your sister sometimes too? Mom is probably just trying to prevent war.