Welcome to GT..
You say "playing the Notes" Assuming you mean working on scales not chords.. It would be a little more help if you were specific of what you are trying to do. We can not see you..
You say your finger nails are Pretty Short.. I would say mine are Extremely Short.. And they need trimming. To me, if I can pick up a pick from a flat surface, they are too long.
How are your calluses..? If they are still soft your flesh tends to suround the string and dampen the vibration. For a mental vision, compare a cotton ball to a ping pong ball.
What section and lesson of fundementals are you working on..?
Knowing this could help us zero in on where your problem is occurring.
I think it's great that your daughter is learning with you and your family is supportive..
Have agreat day and keep on picking
Gordon