Unfortunately, this isn't going to sound like a pleasant task to you. You're going to have to start over.
You can try using a synthetic steel wool and some mineral spirits to get rid of the stain. Another option is a chemical stripper to remove the stain. Following this you're going to have to sand the table again. You'll want to step through 2-3 grits, gradually getting finer, 150, 180 and finally 220. You could stop at 180 for a hardwood like oak. If you need the stain darker, sand with a garnet based sandpaper. It will have a reddish hue to it. General purpose sandpaper is made from aluminum oxide and cuts scratches into the surface similar in shape to the letter V. A garnet based sandpaper is going to cut a shape similar to the letter U. More area for the pigment to gather, giving a deeper color.
Once you have the table sanded, vaccuum. You can then moisten a clean rag with some mineral spirits and wipe away any dust remaining. Never use a tack cloth. One bit of too much pressure on the tack cloth can leave behind a spot of wax. You'll see that the stain won't cover that spot, it can't penetrate.
If you're table is a soft wood, wipe on some pre-stain conditioner, following the directions on the can. After that, apply your stain, evenly and consistently. After 5-15 minutes, wipe off the excess, evenly and consistently. After wiping off the excess, it should be almost dry. Typically, if Minwax stain is still tacky after 4-6 hours, there was too much stain left behind.
More than one coat can be applied to deepen the color, provided you've done the above process. You'll notice the front of the Minwax Wood Finish product says "Penetrates, Stains and Seals." That last part is what is causing part of your problem with the second coat. Not getting enough of the first coat off, sealed the wood, not allowing proper penetration and drying of the second coat.
If you need a darker color or one not available straight from the can, try mixing colors together. Just do everything in measured amounts so you can recreate the color desired. Test on the underside of the table top. Also track how much you put on and how long you left it on before wiping it off. The keyword is being consistent. I'd wait over night after staining to start the finishing.
The humidity isn't going to help your project drying either.
If you stain tomorrow, you should be good to go for finishing by Friday, at the latest. As for a finish, you have a couple of choices. Spray lacquer or polyurethane. Minwax's poly is a "fast drying formula", taking about 4-6 hours between coats. You'd want to do a couple coats. Spray lacquer generally dries in about a half hour. You can probably do 15 coats of spray lacquer in the same amount of time as two coats of poly. Seems like a lot, but the lacquer will go on much thinner. Minimal, if no sanding between coats, as lacquer melts itself as it's applied. Poly is sanded between coats because it doesn't stick well to much of anything, even itself. Sanding the poly gives it more tooth, more surface area to grip. Because of it's drying time, spray lacquer is better used in a dust prone environment. Although, you should minimize the dust possibility no matter the finish choosen. Quicker drying time means less time for dust to adhere to a wet finish.
Hope this helps.
It is unclear if you wiped both coats of stain. They need to be wiped to prevent excess oil remaining on the surface.
I have often put one color stain over another with no problems, as long as both are wiped. The first stain on will be the dominant color.
I would not panic at only 11 hours of dry time in humid weather. The 4 or 5 hour time span on the can assumes optimum warm, dry weather. Also, overnight the relative humidity goes even higher as the temperature drops somewhat.
If this table is small enough, I would consider moving it out into the sun. The suns' radiant heat does wonders for drying.
What ever you do, do not start varnishing before the stain is thoroughly dry! This is even more important if you are considering using lacquer, as lacquers have very aggressive solvents which can lift the underlying stain or finish.
My preference would be for urethane over a normal non-catalyzed lacquer. Urethanes are much more resistant to
to wear and chemicals, particularly alcohol.
The worse case scenario is that you strip the table and start over. I would give it a fair chance to dry first, even if it takes a couple days.
Worst case is starting over? The worst case scenario would be to apply a finish over her stain that is still "sticky," compounding the problem. Starting over is just that, starting over.
I merely advised to give the stain a fair chance to dry in that extremely humid environment. I also advised to not consider varnishing over the stain until it is thoroughly dry. I will gladly trade 24 hours or more to avoid stripping and starting over from scratch. Granted, the poster does have a birthday deadline to meet which might influence their decision.
Indeed, it is not advisable to even be applying the finish coat in that super high humidity, dry stain or not! It would be even more discouraging to get that far and then have to start completely over because the finish coat "blushed".