S.B.
Well, in my opinion, there is comforting when a child needs it and then there is getting a child up because she wants to play and be awake.
At 2 years old, I think you will do well with checking and comforting, patting her back, still in her crib, and telling her that everyone is nigh-nigh and she needs to go back to sleep.
Kids really can self soothe. Give her a stuffed animal and a little blanket and encourage her to get her "baby" back to sleep.
My kids were both really good sleepers, but when it was time for bed, I told my son that his puppy was tired and needed to go to sleep. He held and rocked his stuffed puppy, sang to it, covered it up and konked out.
If your daughter is wanting you, that's okay. Go in, comfort her, tell her mommy isn't far away but the world is sleeping now. You love her and you'll see her in the morning. Pat her back, cover her up or whatever makes her comfy without picking her up, and go back to bed. She may cry, but she will be okay.
Give her a "baby" to take care of and put nigh-nigh. It really worked with my kids.
They do learn that just because they wake up, it doesn't mean the the world has been turned on and is ready to go. I am certain some will say to just put her in your bed, but that can become a habit that's hard to break.
My kids could sleep anywhere. We travelled a lot so they were just accustomed to different environments. Sometimes they slept with me in hotels, etc, but at home, they slept in their beds. But, they would also sleep through the night at Grandma's house in a strange bed or camping in a tent.
It just takes practice. Crying is hard to listen to, but kids can learn to go back to sleep if you don't get them up.
This is just my opinion.
Best wishes.