As Roy says there is only the single pump, if all the forward gears work but no reverse and it is rattling and whining, the likely culprit is still internal to the transmission and I doubt a fluid change would do anything simply because if it was fluid related there would be issues in the forward gears as well. The 4L60-E you have has a few known issues and the sun shell is one it has a few symptoms, if the splines strip it can cause loss of reverse but usually a loss of 2nd and 3rd as well. However if it simply cracks through the shell it will cause a loss of reverse and noise, another is the reverse clutch pack coming apart or the snap ring that retains the reverse input drum has come off. The snap ring usually causes the loss of reverse but no noise or shudder. In all cases I would expect the transmission needs a rebuild.
The attached is what the internals look like on that transmission. The reverse input clutches are part #110 the snap ring is #892 and part #624 is the sun shell.
Image (Click to make bigger)
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Sunday, December 6th, 2020 AT 2:47 PM