How can I send Orana to the Chantry?

No, no. The pleasure will be all mine.   

I'm not really following the discussion, but do want to throw out this fact.

If you recall the conversation you can have with Mother Giselle, you can ask why only human women are allowed to be Chantry priests. From her response, it doesn't seem like elves have any place within Chantry hierarchy. Leandra sending her there would not be to join as an initiate, but simply to receive charity from them, which would be temporary.

Even aside from the various religious objections some have, this isn't really a help to her in that it's not a real solution to her problem, just as giving her a handful of coins is not. She's a homeless Tevinter elf, a former slave, that has no knowledge of the South or how things work in the real world. Other than her ability to work, she's like a child. Truly, the best place for her is with the Hawke family where she will be paid for her work and not abused. She can acclimate to the new life at her own pace.

In Kirkwall, of course, nothing!

Now seriously: How many chances for an elf to become a sister/mother? No much, before Leliana. The other possibility is the Alienage with some coin with a Chantry work (if they don't have enough worker) or a Chantry maintained workhouse/poorhouse – I don't think, this is a nice, safe place. 

Perhaps I just don't really have faith in this Chantry.

The wiki doesn't mention someone saw Orana as a sister in the Chantry, only, that Leandra said, she sent her there. Seems she not even say, that she spoke with Elthina or some other revered mother:  "You can also set her free and tell her to speak to your mother for help. If you pick this option, your mother tells you that she has sent Orana to the chantry." 

Now I want to see her there.

I kind of like hiring Orana as it adds an extra person to the Hawke estate. On the other hand it leads to that bloody bug where Leandra thinks she's a slave even if she isn't. Grrr!

Just get Orana after Leandra dies. Problem solved. 

With a Hawke who supports the mages and wants to build a friendship with Fenris, the best timing of "Bitter Pills" is at the beginning of the Act2. 
But you still can avoid it – if you don't poke Leandra...

I just pretend she meant *former elven slave.