Newbie w/ a question about Intro of Pup

[Willow Oak]

Hi everyone, my name's Chrissy, and first off - I'm sorry to jump in with a question right away.
We have a big family around here, we have 2 cats, 2 kids, and then we have Dewy, a 4 year old Shepard Mix, and Lola, a 5 year old Jack Russell Terrier. Everyone always gets along great, never any problems!
Well, Sunday we introduced Red, a 9 week old Doberman pup to the mix. No issues from Red's side, he's a typical pup
Well I have to admit, it's been a loooong time since I went through the whole "introducing the new pup" thing.
Dewy is sending me for a loop right now. He accepted Red, from what I can tell, he has no issues with him roaming his house and yard, he lets Red play with the kids at his desire (which is a huge thing with Dewy, he's protective of the kids) however, HE isn't playing with Red at all. Most of the time he just ignores Red. Yesterday when Red would come to him he'd growl, on a couple occasions even showed him the pearly whites.
Today, so far, is just confusing me, he kinda played with him a few times (how much can a 75lbs dog play with a 14lbs pup, lol) but then on another occasion showed him teeth again, and once even snapped at him.
I understand teaching the pup the packorder, and social behavior, etc etc, but where to draw the line, and how I cannot figure out right now.
Dew was 6 months when we adopted him. No problems there. So it's been prolly 9/10 years since I've last went through the puppy intro thing.
I guess I'm just looking for some input how to handle Dew's "negative signals", how to make this easier, how to handle things. And most importantly I'm looking for someone to tell me - Hey, it's normal, they'll be buds before you know it. Or - Yea, that's not right! If I knew where we stand here, I could handle it appropriately. But like I said, I can't figure Dew's mixed signals out right now.
Any and all input would be appreciated! TIA

I've had to learn a very hard lesson here. Until Red gets grown up a bit DO NOT leave him alone with your other dogs. Accidents can happen, and as I said, I learned my lesson the hard way.

[RedHope]

Yea, I'm a SAHM, so the only times they are left alone is about once a week, while we run to the store, and whatever other errands there are to run, so maybe 2 hours.
Whenever we do have to leave the house, Red gets crated. For one, for his protection, and for two, cause he is a pup and prone to chew. So I crate him with some chew toys.

I'm hoping over the next weeks Dew will come around more. I've noticed too that he seems absolutely fine with Red out on walks, and about 50% more lax when we're outback playing in the yard. But then in the house he's a grouch. Right now I'm explaining that with the reasoning that most the time, when we are in the house, Dew sleeps. (YK, in between walks and playing)
With the reassurance that Dew's behavior is normal I'm much more at ease!

So far it's not worrisome. Well, I have to admit, I don't even let it get there. If I see Red's heading for Dew and I feel that Dew may not be in the mood for him, I do remind Dew to be good. Most the time all I need to do there is look at him. I think 80% of his aversion stems from jealousy.

[Seravieve]

Had a similar situation when we brought in Eli and Zeke wasn't thrilled about it. Zeke wore a muzzle for a while when they were loose together. It just takes time. Its been over a year now and Zeke still gets a little over protective of J and sometimes growls if Eli gets too close... But we jut put Z in his place and thats that.
I'd give it some time and they'll adjust.