I'm glad she took your gesture the way you meant it
It sounds like she's thinking, from more recent posts of yours, like she's thinking the grass is always greener when she's with the other person.
Maybe ask him (I think it's you that's facebooking with your s/o's other) if that's how he thinks she's thinking of it. When with you she's always thinking about what it's like with him & when with him always thinking about how it is with you. Ask her about it as well. That might help the two of you sort out what's going on & why she's always so antsy to get back to him when she's only just gotten home.