Most water based polyurethanes shouldn't be that soft. Some points to consider in your case:
- Time between coats of water based poly is typically 4 hours. Most manufacturers recommend sanding the previous coat if the time between coats is 24 hours or more. If you applied the second coat after 24 hours (a day apart, as you said), and didn't sand the previous coat, it might be that the new coat didn't adhere well.
- Was the stain water or oil based? If oil, did you let it cure fully before applying the water poly? Not letting the oil based stain fully cure (a few days at least, preferably a week) will also interfere with the poly adhering.
- 2 coats of poly are typically too little, especially with water based poly (which is thinner than oil based poly and easier to apply thinner coats (which is actually a good thing)). With the faster dry time it is pretty easy to apply 4-5 coats at the same time you could apply only 2 coats of oil based poly.
- Finally, as mentioned by Graphus in the comment, there is a big difference between dry time and full strength cure time. This applies both to oil and water based polys. Most water based polys are dry after 4 hours, but are fully cured after a week or more. Some manufacturers list strength/cure time tables, for example 50% strength in 1 day, 95% strength in 7 days, etc. That should give you a good idea how long to wait before putting the item to use.
As an aside, I like using water based poly for floors (incidentally, also from Varathane) on my projects, inspired by Matthias Wandel from woodgears.ca, and apply 5-6 coats (over a day and a half) and waiting a week before putting the project to service. Testing on scraps, there is a very noticeable increase in strength over the week of curing.
As to what to do now, your're best off with removing the existing poly (which is not adhered well to the wood). You can do this via sanding, scraping or chemical stripping. All of these will probably also affect the stain on the wood as well.
Once the existing poly is removed, reapply it carefully, taking into account the above points.