Could be that your mountings screw the addon installation.
What are your mountings and commands you use to play?

I've tried 2 installations, after each one erasing everything and starting new so there would be no conflicts with old files.
First one was:

[dosbox.conf]
[cpu]
core=normal
cycles=8000
................
[autoexec]
mount F F:\
imgmount G <CD_1>.iso <CD_2>.iso -t iso -fs iso
G:
setup
I installed at F:\WEST.
(The second install was the same only the imgmount line had "-t cdrom" at the end.)

Then in order to run the game I would revert the "core" and "cycles" to auto (it wouldn't start otherwise), then:
F:\
cd west
ra

As for the Counterstrike image, I mounted, installed and (tried to) play just like I did with the 2 RA images. BTW, is it necessary to have one of the Red Alert CDs in the CD-ROM/mounted to be able to install CS?
All in all it doesn't go past the Licensing screen.

Mount as c and d and try again (best install fresh to avoid any wrong path settings).
Some programs need a c drive without it they are lost. And tben others need to be installed on c...
So
mount c f:\
mount d cd1.iso...

I installed it. Thanks!

No problem, great that this worked

I faced a similar issue when installing Counterstrike addon.
I mounted allied cd as D, soviets CD as E, counterstrike addon CD as F and aftermath addon CD as G.
I could install RA from allied CD and run the game. But I faced the same issue when installing counterstrike addon.

If I only mount counterstrike addon, I can install it.

So maybe it is mandatory to install from D.

So I observed that Couterstrike and Aftermath cannot be installed if the other CDs (Soviet & Allied are mounter).
However, Countrike can be installed if Aftermath is mounted and vice-versa.
The CD drive letter is not important.
Once the game is fully installed, you can mount all the 4 CD and play missions from each and every CD.