This is completely normal. Although.. I have to admit, if I were you, I would NOT have gotten a second female. When getting a new puppy, it's a good idea to get the opposite sex of whatever you have (it reduces sexual competition and thus means less fighting).
That being said.. If taking the female back in exchange for a male puppy isn't an option, Arwen will likely get used to the new addition. Just realize that she may never LOVE her (and she doesn't have to). Right now she's just making a very clear statement to the puppy: "I've been here longer than you and I'm the boss." Let her do it. As long as she's not attacking the puppy, it will be fine.
I would definitely make sure you get the new puppy spayed before she goes into heat, though. All those hormones tend to make two females get really snippy towards each other.. (There's a reason we use the word "bitch" as an insult!
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Zoey (my Jack Russell Terrier) used to steal toys from Teddy, push him away from me, growl at him over food or treats, etc. She did try to give him a warning snap to tell him to back off from certain things. For that I would put her out of the room for a few seconds and let her back in when she was calm. She was allowed to growl, show her teeth, take stuff away from him, push him around a little bit.. but she was NOT allowed to corner him, bite him, pin him down, etc. Nothing that could physically hurt him or traumatize him. The rest of the stuff, even though it seems mean, is her way of communicating that the puppy is below her on the totem pole. Eventually Zoey became best friends with Teddy. She only bullied him for the first two weeks or so. Then she started keeping her distance and was pretty much disinterested. But after maybe a month she started to play with him, groom him, sleep curled up with him, etc.
If you keep her from doing what she's doing, it will take longer to establish a hierarchy, and you might just exacerbate the dominance issue when they're older because they never had a chance to work it out on their own. Right now, Arwen is training the new puppy. You need to let her do that while also keeping the new puppy safe. I know it's human nature to want to protect the weak little puppy, but you need to communicate with Arwen as her partner. Don't scold her for expressing her dominance, but let her know when enough is enough (for example, if the puppy has gotten the message and backed off but Arwen is still pressing her).
Until they're friends, you need to keep them separate while you're not there to supervise. If Arwen is allowed free run of the house, don't change her routine on her by putting her in a room or a crate. Instead, put the new puppy in a crate (it'll help with house-training anyway). That way Arwen can't hurt the puppy when the new puppy is hassling her to play and her nerves are frayed. It happens to the best of them.
Don't worry, this is all normal. Some pairs go through it and some don't. It just depends on the dogs.
my chi is being really mean to the new baby
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