Continues to bark at mom....why?

Does the pup really like to be picked up?
There's a chance that you've got a clever puppy on your hands, and she knows how to get what she wants - by barking [] If she always barks at your mom and mom ends up picking her up, the dog has learned that barking = being picked up. So if the pup likes to be picked up, it sounds like she's already got your mom trained! 

Do you think I should tell her to use the NO BARK method, Because the NO CHEW METHOD worked ?

I think if I was in your situation, I would just ignore the dog. When she doesn't get what she wants, she'll stop.  You could try "no bark", if thats what works for your dog.

My mutt, Sierra, actually does pretty much the same thing to my mom.

A little history:
I got Sierra when I was 16 years old. It was a joint venture with my 20 yr old sister, and it was against my parents will - especially my mom ("dogs don't belong in the house!"). But my sister and I wanted a dog, and this puppy had no home, so we gave it one.
My mom slowly warmed up to the dog, and (when she thought no one was looking) would play with her. She'd try to stomp on the dog's toes, and Sierra just loved it.
I've since moved out, but EVERY time Sierra now sees my mom, she goes into a barking fit. Her tail wags, her whole body wiggles, and she barks her head off. And every time she does this, my mom goes and tries to step on the dog's toes.
So Sierra's got my mom trained too, but there's really nothing I can do to stop it - my mom likes to do it, and Sierra just loves it.
However, I am certain that if my mom just ignored the dog while she barked, Sierra would eventually stop. Barking would not serve the purpose anymore.

Dogs are smart, so if you've got a really smart puppy on your hands then you'll have to make sure you watch what you (and your mom) do from now on.

Hope this helps. Good luck! []

Thanks a bunch [][] for you help. 
have a nice evening