Of course V changes when you raise T. You clearly aren't understanding. No surprise there. Here...step by step....P and V are inversely proportional...know what that means? Increase P get a decrease in V...increase V get a decrease in P. If you want to increase P or V without reducing the other, you must A) increase (n) B) Increase R, or C) Increase T...the product of rRT will then increase to equal the increased product of PV.....with me so far?
So far, all good.
The AGW hypothesis claims increased greenhouse gasses cause T to increase, which results in an increase in V in order to both sides of the equation balanced....As you said, increase T and V increases. That is apparently where you stopped thinking.....the problem begins with that increase in V which causes a reduction in the density of the atmosphere (r) which must reduce the product of nRT. Get that? The two sides of the equation must balance.
PV = nRT
T went up, so V went up. It balances just fine. Density can change, but there's no density term in the ideal gas law. P doesn't change, as we'll discuss below.
In the real world, a reduction in (r) will result in a reduction of P also because less mass in the atmosphere will result in less pressure if gravity remains the same....is gravity changing?
In the real world, the taller air column balances the lower density, keeping pressure the same.
We know from direct measurement that P is not, in fact changing at the surface even though the density of the whole atmosphere changes when V changes. Still with me?...because we know that P isn't changing at the surface, we can't balance the equation with a reduction in P that results from the reduction of (n).
Again, there's no density term in PV = nRT. V went up, T went up, everything else in the ideal gas law equation stayed the same. It balances just fine.
I'll also note you're torturing the ideal gas law, which is derived by starting with the assumption of a system with the same conditions throughout. It's not correct to try to apply the ideal gas law across systems with gravitational or pressure gradients, so the whole discussion is really moot.