Honestly, I'd recommend getting a decent used bicycle. 2 miles is nothing, especially once you get acclimated to riding. Last weekend I rode down to my local bike shop (about a mile and a half away) to buy new pedals for my MTB (Black Ops Squatch btw, they were $12 and I picked them up after someone here recommended them as good budget pedals), decided to go on a little test ride, and kind of ended up riding 20 miles on accident.

Great exercise and you can haul stuff with them too!

I know that isn't necessarily what you were after but at that price range, I think you might struggle to get anything reliable. That said, if you really want a scooter, keep an eye on slickdeals.net under the sport section, escooter deals pop up regularly on there.

Gotrax is definitely not reliable as a company and I regularly see people complaining about them fwiw. That said, you could probably just find a higher capacity battery for your existing scooter if it's otherwise functional.

Save the ewaste and buy a new battery?

Could it be the quality of the cells thay made it cheap and not the efficiency of the motor?

Switching to a pedal assist bike could help with the range of you are open to expending some of your own energy.

Slightly off-topic, but if your current scooter has inflatable tyres, I suggest you check their pressure. The drag gets considerably higher with underinflated tyres, making your battery discharge at a faster rate.

i dont know where you live but these can go below $500 and have 50km range. these things are huge in south east asia so if you can reasonably import them then i highly suggest research them and consider them. these e bikes also have in bike configuration called cyrusher in western i think but its way more pricier. if you can, try getting them from asian vendors because its way way more cheaper

This entire answer is mostly conjecture, but I think you'd have to be looking for the e-scooter that has the largest battery pack in that price range. Of course, such a pack would add weight and possibly bulk to the scooter. A quick search on Amazon showed this scooter, a Segway NineBot ES4 listed for $480.

Your GoTrax has a 36V 5.2A battery pack, which works out to be 187 Wh. The ES4 has double the capacity, at 374 Wh. If the GoTrax could only muster 4 miles, then the ES4 should be double that.

But I do think there may be something wrong with your GoTrax. 187 Wh per 4 miles means an efficiency of 30 Wh/km. But scooters tend to be closer to 12 Wh/km. For reference, a class 3 ebike cruising at 45 kph (28 mph) is 48-60 Wh/km. Scooters travel so much slower, and so should be many-fold more efficient.

If we say 12 Wh/km is too optimistic for the ES4, then let's conservatively assume it does 24 Wh/km. That would still mean it could do 10 miles, which is just within your parameters.

AliExpress has scooters in your budget that advertise further range, but I haven't tested them personally.

Have you considered getting a bicycle? For these distances you don't really need any engine unless you have a physical disability.

2 years ago when I searched, I was unable to find such a thing, because I needed to do 10 miles twice a day, every day (although I could charge between). I spent about $2k for 25 mile capacity.