Pretty much that's all Regina had to do. Emma made it clear in the beginning she wasn't planning to stay. She planned to drop Henry off and leave which she did but wasn't able to leave town. When she talks to Henry later she's still pretty supportive of Regina. She only ends up staying when she realizes Regina's lying about loving Henry. At least from Emma's point of view Regina only had to act or show for a week that she really did love and care about Henry. What does she do? To show she's a great mom? Gets Emma set up to be arrested, goes to Henry at school to tell him about it and try to convince him Emma's bad, and then sets her son up to be crushed by having him overhear Emma saying she thought he was crazy. What? You mean that didn't work? Who would thought? Except you know pretty much everyone. Regina showed she didn't have Henry's best interests at heart or had no problem hurting Henry to get what she wanted. When Henry runs off crying Regina just sits there with a big grin on her face. Henry's not the one who convinces Emma that she needs to stay a week and then longer. Regina's the reason Emma stays. Had Emma seen what you suggested Regina making Henry pancakes on Saturday and hanging out with him all day and just showing that she loved Henry. Emma would have thought everything was fine and left. Not only did she not do that it never once seem to occur to her.