it is in terrible shape in the kitchen
High-traffic zone there, consider a rug or a runner to lesser the wear and tear on the floor at that point.
Does anyone have any suggestions for a way to harden and finish the wood so it will last?
The issue really isn't as much to do with the wood as with the finish. Although pine is a relatively soft wood it doesn't look like the floorboards themselves have weathered poorly in the photo, it's mainly the varnish.
Now to be fair to the varnish it's not its fault that it began to flake off, ALL floor finishes (all wood finishes period) regardless of cost will fail eventually with cleaning and surface wear. What you weigh is a balance between cost, ease of use/application, looks, level of protection, wear characteristics (resistance to wear, wear modes) etc.
So hardening the wood shouldn't really be a primary thought and many finishes will be harder than the wood itself and will toughen up its surface somewhat. Pine floors are innately softer than hardwood floors and a certain acceptance of this is a must if you have them. Pine will collect dents and scratches more easily. On the plus side with floors they are nearly universally full-thickness boards, not merely a surface veneer glued to some substrate. This means pine floors can be sanded down and refinished many more times, giving working lives of a century + instead of a few decades, at best, for laminate flooring1.
but I don't want to waste a ton of money and time doing it just to find it is not going to be able to wear well regardless of the finish.
First thing you need to get your head around is the need to sand. Unless you fancy sitting on the floor for hours scraping the surface like they did in the 19th century the only way to refinish a floor is by sanding it (see this previous Answer for more on that, How to fix a wooden floor).
Now, what finish?
There are many options available to the homeowner today on floor finishes but they fall into two broad categories, penetrating and film finishes.
Broadly speaking the former will age more gracefully than the latter. With film finishes — your floor currently has one of those on it — once they fail they begin to literally flake or peel from the surface starting from any minor point of damage. With penetrating finishes you get a much more gradual failure mode, where the finish more slowly wears down to the bare wood across an area.
This seems to argue in favour of the penetrating finish, however there's a catch. The better film finishes will wear a lot longer, years longer, before they begin to fail when in the intervening period penetrating finishes would mostly (invariably?) have begun to look tired in high-traffic areas.
A penetrating finish can be topped up easily enough, but on a surface the size of a floor this needs to be looked at realistically2.
In addition to this, film finishes provide better protection from water, wine, coffee, beer, pet accidents etc. because the liquids basically never get to the wood. You can't ignore spills without consequence with most penetrating finishes (manufacturer claims notwithstanding) which can be a major consideration for those with a very active lifestyle and/or with kids in the house.
A word of warning, while some floor coatings available now from the big names in finish are modestly priced some finishes (typically from 'boutique' makers or imported from Europe) are eye-wateringly expensive, so expect some sticker shock when you get to searching in earnest for what you'll use!
The number one reason floors wear poorly is from tracked-in dirt and grit from outside3. If you ban outdoor footwear from the majority of the house your floors, regardless of what they're finished with, will last a lot longer in good condition.
1 Many laminates can be sanded only two or three times which at least the manufacturers are upfront about, and it's why those flooring options are relatively inexpensive.
2 It's still basically refinishing the floor. Easy to spend an hour "freshening up" a tabletop or countertop every few years when it needs it. Can be quite a different story doing a floor even in only one room.
3 Number two is from overcleaning. This tends to be a consequence of reason #1 so you can still blame outside dirt if you want.