Toyota Repair: 1998 4Runner Transmission or Differential problems, differential problems, rear differential

Question
I have a 1998 4Runner SR5 model- V6, 4 wheel drive, about 250,000 miles, automatic. I park on a slant, where I back up out of my spot onto a hill, and have to drive up to then leave my street, but the parking brake is not engaged in my spot. I noticed it occasionally "kicking" after a slight pause a couple months ago, when I would back out of my spot, be at a slant (nose up, tail down) on the hill, and then put my car in drive to go forward and press the gas pedal. I got new tires (had to do anyway, not related) and when I took them to get balanced the guy said that the left rear brake was sticking... my friends' husband, just to be safe, changed my transmission fluid, gaskets filter... it started to get a little worse, so my dad took the wheel apart and changed the diff. fluid, seal and bearings on that side (left)... he said the fluid had leaked into the brake drum, and possibly was causing the brakes to "stick" when I was backing up my car, and then putting it in drive. He drove it back to my house (4 hrs away) after fixing it this past weekend, and in the past 4 days of having it home it is a LOT worse... now it kicks HARD and takes about 30-45 seconds of my revving the engine to get it to "go" when I put it in drive, and it's done it slightly at a couple lights, when I've been stopped and am starting to go. I took the tire and brake drum back off to check for leaks but it looks good- no leaks. Just now, on leaving a restaurant, I slammed the brakes on to re-set them, and when I tried to go, the entire front shuddered and kept jerking... my husband said it was the trans slipping... and we needed to make sure the back was set, so we reversed, slammed the brakes, and tried to go... it shuddered and we had to put it in neutral, then into drive before it would engage... after more slipping. The rear brakes also feel "sticky"... why would it get significantly worse after working with the rear differential? Is there a way to adjust bands on my transmission or will the entire thing have to be replaced? As you can see, I know just enough to be dangerous. Is there anything else I can do, or should check before assuming that it IS the transmission, at this point? Thanks, in advance, for all your help!

Answer
It does sound like a transmission problem if it takes that long for it to move after putting it in to D, the shuddering also would indicate the same, there are no bands to adjust on this transmission but you can check the throttle pressure cable attached to the throttle body where the accelerator pedal attaches it has two 14mm nuts that can be adjusted but more important remove the cable and make sure it can be pulled out and that it goes back in by itself and is not sticking. If this helped please click on the "donate" button, any amount is welcome.