I think you are BOTH totally normal! :)
Of course, it's normal for your DD to really like going to your mom -- if she's anything like my mom, my DD adores them and always has fun with them. Also, she is at that age where she is really starting to open up and notice the world around her. And since she's likely with you more, grandparents are a novelty!
Also, I do think it's normal for you to feel a little jealous or possessive. That's YOUR baby, after all! I'm sure especially with nursing you two have formed a strong bond. So seeing her want anyone but you at this point can absolutely be a little disconcerting! You're a human and you have feelings, too - so kudos to you for recognizing that and not letting things get out of control.
Big picture - this is a good thing. You and DD will always have strong ties to one another; that goes without saying. Also, as she gets bigger she will have another woman in her life who she feels comfortable with and who can be a role model to her in her own special way. And honestly, what more could we want for our children?
Hang in there! And don't feel guilty or selfish. I truly think all of this is a natural thing and part of the parenting process.