Disclaimer: I don't own Once Upon A Time and never will. No copyright infringement intended.
Emma Swan has never been anyone's priority and she's reluctantly gotten used to that fact. It hurts, but she's learned to live with it. Now someone is putting her first, and she's not sure how to deal with that. It's surreal and makes her want to cry, which she hates with a passion. So she reluctantly gives in and lets her mother hug her because she needs it at that moment. It's nice to really let go for once. Emma feels at home in Mary Margaret - Snow's – arms and she never wants to let that feeling go. But they have to pull apart and head back to the island with Mulan and Aurora.
She tries not to grieve for the life she could have had and hates Regina even more for casting this curse, for taking this life away from all of them. Emma can imagine what her nursery looked like before it all fell apart, but she bets it doesn't live up to the reality. She's a princess (something that is still hard to process) and she could have grown up here. Emma is falling apart at the seams and trying desperately not to because she needs to be strong. This place isn't like her world and there's danger lurking around every corner, as cliché as that is.
God, she can't believe her life now. Her parents are Snow White and Prince Charming, and she's met Sleeping Beauty and Mulan. Facing down an ogre was terrifying and surreal, too. She misses Henry and is terrified of what Regina's mother is going to do. While Regina's behavior isn't justified, it is now understandable after having met Cora. The apple doesn't too far from the tree, which she wants to laugh at for the irony, but can't because it reminds her that she almost lost Henry. She's grateful that "True love's kiss" seems to work.
And then Emma is reminded of August. He had died, too, and she has no idea if anyone even knows. Maybe magic coming back to Storybrooke brought him back, too? She hopes so. Despite the fact that she didn't believe him at first, he was a good friend – with the possibility for more – and she doesn't want to lose August for good. Plus, she has a good arsenal of Pinocchio jokes stored up and wants to use them. (She feels guilty that she has them in the first place if he's still dead.) That's when she remembers Graham. Henry had said Regina killed him, and now Emma realizes that must be the truth. She squashes down the anger because she's sick of it and there's no time for it now, especially when Aurora's angry enough for all of them.
The urge to cry because she is someone's number one priority returns, a feeling Emma curses. She's sick of bouncing back and forth between anger and wanting to cry all the time. For the first time ever, she thinks she may be able to forgive her parents for leaving her on the side of the road. She understands now why they did it and can't wait to talk to them about it when she and Mary Margaret – Snow – (She really needs to figure that out) return home to Storybrooke. She wants to hear more stories about them, the ones that weren't in Henry's book. Emma still can't believe that she's loved enough that someone put her first. She didn't think it would ever happen until now and she loves that feeling.
However, Emma is terrified that now that she has the love she's been craving all her life, she's going to lose it. She's never been able to hold onto anything good for very long, except for her blanket, which she suddenly misses. She hopes Henry and David – no, Charming, (Damn it, she really needs to stop that) are keeping it safe. Emma's hoped before, and it always turns out badly. Henry's father was an ass and she's glad he never found out that she was pregnant. He cast her aside the minute he got tired of her. Not one of her foster parents kept her because she was a "bad seed".
She tries her best and it's never good enough. Soon enough, Snow, Charming, and Henry are going to realize that and do exactly what everyone else did. Emma wants to believe that this time will turn out differently – and it already is – but she can't take that chance. It always blows up in her face anyway, and why should this time be any different? These people may have gotten their happily ever afters – or they had until Regina cast the curse – but Emma doesn't have one and will never deserve it. That's just the truth. It's especially hard to believe in a happily ever after since she's been alone all her life.
It's been nice to have a purpose and stay in one place, but that ended too when she and her mother got ripped away from their home (Or is it just her home? She's not really sure) because of that stupid hat. And she's glad, but feels really guilty that she followed her into the hat. Emma's the idiot who messed it up somehow and got sucked into this world, and now Snow White has to deal with the consequences of her actions. That'll probably happen a lot before her parents and son are finally fed up and kick her out. She brought the ogre down on them earlier when she fired the gun, and while it's an excuse, Emma's new to this place. She desperately tries not to wonder what else she could and probably will fuck up because there are probably a lot of options in Fairy Tale World. (Does it have another name? It probably should, since they're not actually fairy tale characters here.)
So Emma's going to take what she can get for now and absorb all the love that Snow White has been heaping on her since the curse broke. She's selfish and desperately needs it, even though she doesn't deserve it. Her parents most likely won't put her first for very long after this, especially when they have to deal with other problems.