You are in a difficult predicament. The trans has high mileage, the kit only will address part of the issue, the other parts, at least here in the USA, are hard to find and may not be available, and a proper overhaul requires tools you won't have (such as for ensuring correct bearing/shaft/gear preloads/spacers). The question is: will the trans work
good enough if just the kit is installed (and done correctly - there are several critical steps involved). I don't want to discourage you from tackling it nor discourage you from keeping the car given the personal connection, but I would estimate/expect a 40-60% likelihood of success. Your options are to (a) follow
@12GLS3.5 's advice in post 5, (b) try to find a Hyun reman trans with a new torque converter and replace your trans cooler hoses (and clamps) and flush the cooler's channels (in the bottom of the radiator, using Hyun's flush product) before filling the new trans, (c) try to find a good used low-mileage trans and torque converter and replace your cooler hoses and flush the channels before filling the used trans, and/or (d) take the time to research the availability of the overhaul parts - new bearings throughout the trans, new clutches and discs and wave and return springs (correct quantities of each), probably new clutch retainers for their pistons, new kickdown parts (band/drum/rod/rod retainer/piston/sleeve and probably switch), new o-rings/D-rings/seals/gaskets/filters (these come in their own Hyun kit and generally are available), new solenoids, new (or useable) OD gear shaft, and output shaft locknut. Option (d) will be instructive because it will reveal what is and what isn't available. If you get a good used OD gear shaft, heads-up: Hyun had 3 different lengths. Yours must match.
The input shaft speed sensor (pulse generator "A") likely is not among your main issues. It is, however, reporting - or trying to report - the signals from the misaligned end clutch retainer. I would recommend it be tested (by backprobing BOTH of it pins and connecting the leads to an o'scope) before deciding to replace it. Its signal will increase in amplitude and frequency as the input shaft increases speed, and its signal should be quiescent when the car is at a stop. If option (a) is pursued, ask the trans specialist to remove and clean the
pickup ends of each shaft speed sensor, while the overhaul work is being performed [or if options (c) or (d) are pursued, do that during those also]. The shaft speed sensors come (already installed) with Hyun's remans, so these steps aren't necessary for option (b).
If you decide to tackle the kit job only, get the new (or correct-length useable used) OD gear shaft ahead of time. Also, go s l o w l y when you remove the left cover (or double end cover - Hyun had two configurations there), so you don't dislocate the OD parts behind the left cover before you can see them. Some will want to fall out/down. You will need to know their orientations for reassembly. Also, you will need - want - new o-rings for the bottom of the left cover. There are small holes there c r i t i c a l for oil routing to the OD retainer - for 4th gear. Also, be sure these holes are NOT blocked by any cover sealant, when s l o w l y reinstalling the left (or double end) cover. Also, be sure to use the proper fluid at the end when refilling the trans, and do not over- or under-fill. Finally, bear in mind, the end cover bearing (which you will see when the cover is removed) and all the internals of the end clutch retainer and the end clutch hub (which slides out easily) will be worn. Now would be the time to replace all of these, IF the kickdown parts are
holding in there.