Dimitri is so single-minded in his hatred of the empire that he should be willing to use the Alliance to get closer to the Empire

That’s a logical decision though, and Dimitri has lost most of his logic. No logical person mutilates someone. No logical person blames a 13 year old for a tragedy.

He is willing to go to Edelgard by himself if he has to. He just wants to get her as soon as possible, and couldn’t care less about making allies.

Or at least that’s what he claims. It’s clear he has no idea what he wants anymore.

Claude doesn’t have much room to work with Dimitri. He’s busy keeping the alliance neutral, and in all honestly Dimitri on his own wouldn’t benefit him much. If he were to use Dimitri to get the kingdom back for him then maybe, but then he’d have to worry about a counter attack from the empire, as we see in AM, which would probably result in him just being killed if he didn’t plan out the pincer attack. The fact that Claude sent that letter BEFORE it’s reclaiming shows that he wouldn’t have had time to send it had he waited a second longer. That’s how bad the alliance situation was during AM, and working with the broken kingdom would just put him in jeopardy.

Also, we don’t know what could cause the alliance to lose balance. Joining with an anti-empire party as extreme as Dimitri is could cause chaos for all we know.