introducing pup-help me figure out dynamic?

Hi everyone. This is going to be a bit long, so bear with me. I posted an intro here about the 6 month old GSD that has just come into our lives. (Stray who followed a friend home and wouldn't leave). He is great, and I really want to keep him, but I'm concerned about how it's affecting my first dog, Dizzy.

She is about 4-5 (not sure, she was an adult stray/rescue as well), we think some sort of Aussie-X. She is a very easy and mellow dog, and has been since we've had her. She goes everywhere with me, is never on a leash unless we're somewhere it's required, and is just an incredibly polite, quiet and well-mannered dog. She's not timid, but standoffish with strangers, and will usually prefer to avoid confrontation. She generally doesn't shy away from correcting younger, bouncy dogs who get in her space, but will more often walk away if something's bothering her (like my toddler).

I'm trying to figure out the dynamic between her and the new GSD, who we're calling Cyrus. I don't want her to feel displaced, and want her to be the alpha. To this end, I've designated the bedroom and the bed, and my husband's study where she hangs out with him as Cyrus-free zones. He is very good about staying out, and Dizzy has tended to spend most of her time in them. I feed her first, and llet her in doors first, keep him on the leash while she is off. I have a horse, and Dizzy still comes to the barn with me without him, where she can play with her Jack Russell friend and go on trail rides with me and my horse.

She is going OK--it's only been a week that he's been here--but she's not particularly happy about it. Every once in while she will correct him if he's in her space, and he'll go lie down, but mostly she'll just stay away. If I try to pet her, he will come over and try to get between us, and even if I push him away she doesn't want to deal with it so sighs and walks away. He'll also try to "herd" her around the house, following her around at her shoulder. She doesn't seem to mind, and usually just goes upstairs. There are other times, though, when she corrects him, and I think she "wins"--he will lie down or go away.

Sometimes she will growl at him when he's trying to push her around, but keep her head averted. I'm trying to figure out if this means she's submitting or correcting him. He'll be looking straight at her, ears up, and she'll look away growling.

Things are better when we are outside or on walks. They are happy to trot shoulder to shoulder, either on leash or off, and a few times have actually played chase while we were on the beach or in the park. At home, though, she won't really play when he's around. She's not a big player, anyway, but she always enjoyed playing tether ball with us in the back yard. Now she won't play unless Cyrus is inside with the door closed, even though he doesn't try to play, just lies down and watches.

I'm sorry this is so long, I'm just trying to figure out if Dizzy is letting herself be bossed around by this big puppy, and if so, if that's all right, in terms of both his development and her happiness. If she is going to end up depressed about having Cyrus around, I want to start looking for another home for him before he gets too attached to us.

Thanks for any insight anyone can give. I've always had a one-dog household, so I don't know how to interpret what's going on, or how long this adjustment period will be.