New puppy to home with 15 month old dog

[Garnet-girl]

we have a 15 month old golden doodle (Lola) who was the center of our lives. She never really learned bite inhibition and is still all about her mouth. Never bites, but has her mouth on everything. Constantly mouthing our hands, even tho we say no and try to not allow this.
We just got an 8-week old golden doodle puppy. Lola was jealous and is extremely rough with the pup (paisley). Lola will roll the pup, chase her, put pups head in her mouth and be rough.
We have been intervening, as she is just too rough and I am afraid the pup will get hurt.
We've had the pup for 4 days.
On day 2, pup began fighting back. Showing teeth, barking and snapping.
I am concerned with both dogs behaviors. I hate seeing this very sweet pup showing her teeth, and I hate how rough Lola is to the pup. Friends say "let them work it out". I'm worried. Please help if you have advice. Thank you so much.

 

[Alpha1]

How is Lola when interacting with other dogs? I don't have much experience with pups behaviour but I know that when you bring two of them together, they will most probably play. Sometimes this can get rough and it may not be easy to tell if they are playing or fighting. Hope you get the help you need.