Yes - one thought especially; It WILL get easier. The fact that your daughter does not exhibit these difficult behaviors around others means that she has learned proper behaviors and can carry them out outside the home. At home, just like you and I do sometimes, she feels she can "let it all out." Home is where she feels safest and has the most understanding. Her little girl brain is probably saying "I know I have to spell everything out for Nana and Papa, but Mom and Dad know what I am trying to say all the time, I don't have to try as hard with them." It is probably very difficult for her, her inability to communicate clearly, and she just wants to "relax" and not try as much in the comfort of her own home.
Even though she is two years old, she is still just a tiny little baby, a little girl who has not developed all the skills that some or most children have at her age. And, just like all children grow at different rates physically, emotional (emotional=behavioral) skills develop differently and at different rates with each child.
Trust me; I understand your frustration! Your experiences sound VERY much like my own! I stayed at home with my two children, (one typical daughter, and a son with special needs) until they started K and it is VERY tough! At the end of the day your emotions are totaly drained. There was one time I went down into the basement (where our garage enters our home) and waited there with a note for my husband that said "Don't look at me, talk to me, or ask me to do anything for you or the kids tonight. Just leave me alone" I was just so done with being "needed!"
One of the hardest things that stay at home parents encounter is that we often have higher expectations for our children; especially when they are younger. We think "I'm home with him/her all day - I teach them right from wrong and manners etc, they should be "at this level" all the time. We expect them to be more advanced emotionally and academically than a child who is in daycare or who does not have a parent as their primary caregiver. As a result we are often "disappointed" when our children act just like little Johnny down the street and make us feel like all of our hard work is for nothing! But, they do learn, and they do get easier. Just not at our pace.
If you have stopped your Baby Blues meds you might consider going back on them. For me; it wasn't saddness that was the biggest symptom of my blues; it was this anger that was always boiling just below the surface. Keep up your great work with your daughter! It is obviously working, and will soon be demonstrated at home also.