As far as his assumed 'incompatibility' with Rain is concerned, I think you gents who are putting down Uridimmu forget that his fragments/Marchosias do the bidding of their summoner. It's not him we have a quarrel with, but the person who summoned his fragment.
It's complicated. Uridimmu is a voice of violence, and he makes
suggestions to lesser men:
But I am and always will be the Hound, the companion to the nightmares of Man, the whisperer of violence in your hearts, the mightiest of the eleven primordial demons.
His fragments are connected to the great whole, and he likely is aware of what his "marked" are doing. He might not be able to control them, but he loans them his power so long as they perform violent acts.
At least, this is my read. What he gets out of it is unknown; perhaps it is his nature and he just can't do otherwise, perhaps it serves some kind of plan. Me, I think the doggo wants out.
I must savour the first offering to enter my domain after an eternity of solitude and hunger.
You wonder to yourself, innocuously and with genuine curiosity, why he is trapped here all alone and hungry if he is so mighty. In response, the six eyes flash in anger, purple flames blazing to the ceiling.
An eternity of solitude and hunger don't make it look like he stays there of his own volition.
But he could also want more people sent to his halls, or something else entirely.
Anyway, even if he isn't the mastermind, it still makes him an accomplice to the murder of Rain's mother, and the attempted murder of Rain.
It's not that he is evil or is actively seeking her death so much as he is a mercenary force employed to kill them, with no objections raised. How much that matters to Rain is anyone's guess; I suppose that if we start relying on the Hound she will find a way to reconcile that rather than lose the one and only family she has.
Also, on the matter of Rain, I didn't see people commenting on this bit:
You take the child in your arms and she clings on tightly, bawling her eyes out, as if she would never let go of you again. "How strange," murmurs the old matron. "She was quiet all this while but started crying shortly before you came back."
It looks like Rain has some kind of tele- or em- pathic connection to us. Or is it to her necklace that we are wearing? It would explain her appearance in the dream.
It lends credence to the theory that the power of her amulet may be a borrowed one.