These two really did keep up a very pleasant veneer to each other. Let’s look a little deeper.
Marie Louise tells Napoleon that she’s obsessed with him in her letter.
She’d be lost without him and wishes she could write letters to him constantly.
Napoleon tells Metternich (the person really running Austria) that he regrets his second marriage.
Whatever happens, Marie Louise writes that her father, the Emperor of Austria, can count on her to do whatever he needs done. She is also afraid her lack of love for her son is obvious from her physical cues.