OP, reading your responses, there's a lot more going on here than whether your DH brings stuff home for your kid.
You feel like he is shirking his responsibility to your family, and that includes you. You need to address this not as a specific thing about how he interacts with your kid on business trips, but about how his business travel (and likely other things) is impacting your perception of his commitment to your family, including your marriage.
This situation will get worse if you only address the symptom, your not liking how he interacts with your DD while he's traveling. I have a close friend who is on the brink of divorce, because after years of fights about his work travel they never addressed the real issue. His wife feels neglected and has lost trust that he cares. (FWIW, in her place I would too.) She also accused him of having an affair, which he did not (I know this for sure)...but now he will admit that for a decade+ he did have a mistress, his job. It's a really awful and painful situation to watch unfold, and you don't want to get there.
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