Does Reiner suffer from split personality or DID? I noticed that during two situations he behaved in an unusual way, which might mean he suffers from split personality.
I noticed this in the following scenes:

When Reiner and Bertholdt kidnap Eren, they sit on a tall tree in the forest with Ymir.
Also when Reiner asks Annie to take the ODM gear from Marco, then cries when he gets devoured by a titan
In a sense, yes.

Reiner's psychological issues resemble those of dissociative identity disorder, in which a person's identity is fragmented into two or more distinct personality states, producing behavior changes and lapses in memory

Reiner's DID type personally started shortly after the untimely death of his old comrade. Reiner began taking on some of their personality and entwining it with his own over time.

 Following Marcel's death, Reiner began incorporating elements from his personality into his own. He became more decisive and assertive, even willing to threaten Annie and Bertolt to ensure they followed his orders, yet also deeply caring and genuinely desiring to protect them
 [...]
 By the time he joined the 104th Training Corps, Reiner had completely incorporated Marcel's personality into his own

Source