Just to clarify, the alt key is working for some of the toons, but not all of them.
And similarly, the ctrl key works for some, but not all.

So the key is being broadcast.
Not sure that the keys are broadcast to all clients.
And not sure on the workaround if it is not.

However, you could try the macro:
/cast [nomod] Big Mount; [mod] Small Mount

That way, you just need any mod key, or the absence of mod keys for the macro.
That of course assumes, at least one mod key is working for each toon.