Don't worry about the aluminum wire, given the ampacity it is surely #4, and aluminum wire of that size is definitely alright even if it's the old AA-1350 alloy. It's probably the new AA-8000 given the 1998 vintage. Clean it up, it should be fine.
The 3-wire configuration was legal up until 2008. Effectively it is legalized "bootlegging ground". As with 3-wire dryer and range circuits, there's a risk, and I gather you've "shaken hands" with it. Ground rods won't fix that. You need to carefully maintain the neutral wire to prevent this problem.
If you want the redundant safety of a ground, the only workable option is to retrofit a ground wire back to the house.
A grounding rod cannot perform that function at all. Dirt does not conduct electricity to any useful degree.
It conducts just enough to cause some milliamps of flow if you touch a hot wire while standing on the ground, enough milliamps to kill you. We reduce that risk by assuring the electrical supply is near earth potential so less current will flow, that's what the neutral-ground bond in your main panel does.
The grounding rod is useful for sinking natural electricity, notably ESD.
This can be done as "just a ground wire" and need not follow the same path as the cable. You connect your subpanel's chassis or grounding bar to your main house's main panel's ground bus or grounding electrode.
Then, you will need to electrically separate all neutrals and grounds in the subpanel. If you are used to just spamming all neutrals and grounds onto the same bus, this will come as a surprise. Some panels come with two bars linked together with a neutral-ground bond which can be separated to make 2 bars. Other panels require purchasing an accessory ground bus and removing the ground bond or screw from the neutral bar.
Any bootlegging of ground anywhere in the garage must be removed. Neutral cannot connect to ground anywhere in the garage (except inside a faulty appliance, but with any luck that will trip the breaker.)
This, and only this, will protect you from shock if the neutral fails again.