I can't be sure from the short clips, but to me this looks like a combination of trained behavior and stress.
Right at the beginning, she moves her whole body to the side and tries to pull her puppy with her. This is avoidance and can be a sign of stress.
Then something distracts her for a second and the owner grabs the puppy. Notice how she repeatedly licks her lips when she notices (sticking the tongue out just a tiny bit). That is also a sign of stress.
The way she holds her puppy between her paws is either protective or possessive. She controls where the puppy goes (nowhere) and who takes her puppy away (no one). It doesn't look like she feels threatened or abused, but a little stressed. If she was afraid that the owner would hurt her puppy, she would have given clear warning signs by now.
Her owner tells her to give her paw, which she does without hesitation. That's another clue that she's treated and trained well and trusts her owners.
Her tail-wagging (as any tail-wagging) speaks of excitement. It could be positive excitement like joy or negative excitement like nervousness, you can never tell the difference by looking at the tail alone. But again, her behavior speaks of trust and maybe a need to control everything.
This is clearly trained behavior. Her owner said something and she performed the corresponding trick. But again, there is stress involved here.
I noticed that she licked the front of her lips and averted her eyes in that instant. That's the same sign of stress we saw in the first scene.
Look closely at her mouth when she licks her lips and when she pants. She draws the corner of her mouth back into something resembling a smile. This is another indicator of stress that is often misunderstood by humans.
Right at the end of the video, she more or less jumps away from the door. It's impossible to interpret because the video is overlaid and ends right then, but it's a rather sure sign that she doesn't feel threatened. It could be another iteration of avoidance (stressed), but she surely wouldn't leave her puppy when she felt threatened.