Maybe it will help if I use your own example.Moving an object directly opposite of gravity is only one of an infinite number of possible vectors, about half of which will work with the force of gravity to increase an object's downward motion, and about half of which will have to work against gravity.
In all cases, F = ma remains unchanged. The amount of acceleration any given mass exhibits is directly proportional to the sum of all Forces acting on it. You are confusing the final vector (e.g. gravity + external force = possible lift) with the individual F = ma calculations.
Here's an example. Assume gravity of 1G, and 1 unit of mass. There is a constant downward acceleration vector of F = 1 / m = 1, or 1 m/s^2.
If I apply an upward force of 0.5G to that mass, then it will accelerate upward at a rate of 0.5/1, or 0.5 m/s^2, for a final vector that is still falling downward, but now at only half the rate. I'm still accelerating the object according to F = ma, just not enough to fully overcome gravity.
If I applied that same force perpendicularly, the object would now have a downward vector of 1 m/s^2 PLUS a horizontal vector of 0.5 m/s^2 (ignoring friction) - I didn't have to overcome gravity at all, which is why you can push more than you can lift (when gravity is a significant factor).
That same principle applies even if you totally remove gravity - I can still only accelerate that mass at 0.5 m/s^2 because the amount of Force I can apply has not changed.
So back to the box if I apply 2 units of force with gravity of 1 unit countering I get acceleration of 1 unit. But if I apply 2 units without gravity I get 2 units of acceleration.
Now let’s slide the box if I apply 2 units of force to slide the box with gravity of 1 unit and friction of say .5 units I only have to counteract part of the unit of gravity since I’m not going directly against it so for simplicity sake we say with the vectors the effect of the gravity is .5 in this case so I accelerate 1 unit to the left if we remove gravity I’m only countering the force of friction so I move the box 1.5 acceleration to the left. If the box is in the air so we eliminate friction (yes I know there are other forces but I’m keeping it simple) the acceleration of the wind is now 2 instead of say the 1.5 we had with gravity( these numbers are no where near correct but we are going for simplicity) meaning the wind is now having a greater effect.
Now for dis structure we have the wind pushing different parts of the ship in different directions and with different forces some of those directions and forces are change very rapidly this can cause torque effects that can rip the ship apart.