I don't think he knows about her trying to steal her power but other than that he should have known by now, and ya that's a jack ass move to pull on your kid after knowing they don't even fully trust you yet
Not just that but he clearly knows she’s in danger and he still hasn’t ACTIVELY done anything about it. Which probably means the empress has a significant amount of power on her side.
He’s the emperor though I would assume with his spiritual ability he should be able to do away with the current empress in some way even if it looks unjust. Despite that he hasn’t done anything. He can’t even see how much danger he put her in. All he wants is to prove she’s the princess for his own selfishness, because like you said rather than prove his love to his daughter by taking care of the danger he is being impartial and just.
So this ah gonna tsay shes a princess then have her live in the same house as her mother's murderer??? The house her mother's murderer practically controls???? The murderer that is actively trying to take her spiritual power?????? Does he think he can protect her in the imperial palace tm where lit anyone whos anybody can hurt her and she'd be cunerable bcus ofc the emperor has to be impartial to everyone. This pos is so stupid i wonder how he survived this long to be an emperor and what tf the empress saw in him.