Aww. Yes mine does this too. My daughter is going to be 4 next month. Most mornings I have to rouse her from bed and drive her over to Grandma's on my way to work. Some mornings are hard and she acts all sad and doesn't want me to leave. I try to be sympathetic but keep it as short a goodbye as possible. "I know it's so hard I'll miss you too!" kiss "bye bye". I think some mornings are just hard. Like, I have those days where I feel so cozy in my bed and it's like "noooooo I don't want to get up I'm so comfortable". I think it's the same for them- "noooo I just want mom to stay and cuddle with meeeee"
I also have a day or two a week where I leave before she wakes because grandma will come to the house and watch her. I do NOT wake her up to say bye on those days. She deserves her cozy sleep, I can allow her that at least one day a week. I don't know if she is ever sad or not, but I don't want to know.
The funny thing is, she NEVER wants to leave grandma's when I pick her up! She wants to stay and play, finish a TV show, go on the swing one more time etc. I think in part is also an age/stage thing... just wishing to control the situation a little bit and not be at the adults whims and schedules.