I love this concept
It's completely impractical and I can readily imagine a number of problems with implementing it — but I love the concept. Honestly, it's the best idea for weather control I've heard in a very long time. Cheers! But, you tagged your question science-based, so let's talk about some science.
Issue #1: Time
Weather is constantly changing, so I foresee this idea solving the problem of big storms, like hurricanes. The idea of using it to keep the weather happily pleasant everywhere on a planet 100% of the time would be a serious challenge as the process of receiving, liquefying, and redistributing the air would take time. If you had the ability to instantaneously (or nearly so) move the volume of air needed about, then there are simpler ways than this to solve the problem. In your second question (@Elemtilas is right, for future reference, only one question per post, please) you mention using a tanker ship. Even if the tanker were sitting around, filled with LATMO (liquefied atmospheric gases), the time it would take to move the tanker into position would mean only the largest storms would matter. The small ones would have dissipated by the time the ship arrived. You'd have this problem pretty much everywhere what wasn't right on top of a LATMO storage facility.
Issue #2: Volume
The volume of air needed to moderate even a small change in air pressure is enormous. A single liter of LATMO converted to gas is 0.7983 cubic meters. A small storm might need thousands of cubic kilometers of gaseous atmosphere. A hurricane might need a million cubic kilometers. Let's stick with 1,000 cubic kilometers. That's 1.25 trillion (yeah, with a "T") liters of LATMO .
Which is a long way of saying that you'd be hard pressed to store enough LATMO to fix one storm in a timely manner. Don't lose hope! Keep reading!
Issue #3: Acquisition
I was tempted to suggest that you import LATMO from interstellar sources, but it wouldn't take long before you increase the average atmospheric pressure and that would have serious consequences for the environment. This means you're drawing air from one location, concentrating it, and then moving it to another.
Where do you gather it from? You'd want to work with multiple locations so that you're depleting a high pressure zone to increase a low pressure zone.
How do you gather a lot of it? and where do you store it?
At the moment I'm imagining an Earth that looks just a little bit like Pin Head:
![enter image description here](https://cdn.statically.io/img/i.sstatic.net/lQx8l0A9.png)
Pipes, which can be used to acquire or to disperse atmospheric gases, dotting the Earth in a way that makes today's wind farms look absolutely childish. That way you can draw the air away from areas where that's needed and push it to where it needs to go. The underground pipe network (the indestructible underground pipe network, which I'd advocate hand waving) has this constant ebb-and-flow of LATMO so there isn't a problem (theoretically) with supply.
Issue #4: Distribution
You'd think #3 solved the problem with #4, but here it's worth noting the problem with mountains and oceans: both of which need whomping long pipes. I mentioned in #1 that it would take too long to move LATMO via ship to a problem area over the oceans. You don't even have that option over Mt. Everest as airborne tankers are considerably smaller than ocean-borne and the cost of pushing a well-laden airplane is much greater than the cost of pushing an ocean tanker with a similar load. This underscores the need for indestructible pipes.
But distribution has another problem. Weather moves. This means the pipes pushing LATMO into the atmosphere in one area may suddenly find themselves sucking atmosphere back in just an hour or two later. Or minutes later. The world just might sound like an old turn-of-the-century carnival calliope without the positive influence of Freddie Mercury.
Issue #5: We actually need storms...
Finally, there's a purpose to storms. I've been focusing somewhat on storms. Let's assume you have an acquisition/distribution system that's fast and efficient! What happens when the world's climate is reduced to an even pressure all of the time? No wind, no storms (although you'd still have rain)...
- Many plants reseed via wind and storm.
- You can equalize the pressure, but not the temperatures, which wind stirs up. You would affect (if not remove) that natural process, which would have consequences.
- You'll confuse the snot out of birds.
- Airplanes have more trouble taking off, flying, and landing in static atmosphere. In fact, I've seen planes at Las Vegas fail to take off because the air was both hot and still. They simply didn't have enough runway to generate the extra velocity needed for the lift denied them by wind and cold.
Having said all that... I love this concept!
Frankly, if you wanted to just deal with tanker planes, trucks, trains, and ships... Cool! It would mean having a smaller impact on only the larger storms, but that leads me to my next statement.
Screw science!
I think the fad of trying to make everything "as real as possible" denies the dreamers! Just because it seems impractical or might have consequences, do it anyway! As I said before, it's the most imaginative weather control idea I've heard in a long time. Use it! And throw everybody the ubiquitous vulgar hand gesture as you take your royalty checks to the bank.