If, as you said earlier, you truly don't mind him doing it at home, then that in and of itself isn't a problem (though it's not really appropriate to be doing it in front of your daughter). However, if you do actually mind and have just accepted it over time, then of course you need to speak to him about it.
I think it's his response to your requests to stop that are the most concerning. If he truly cared about and valued you, I would've thought he'd stop immediately and be extremely apologetic. His getting sulky and groping you in public again do suggest he's only thinking about himself, with no regards to how you feel about what's done to your body.
As to whether he only sees you as life support for breasts and a vagina, none of us here have the full picture of your relationship. You say he's very caring, what does that mean? Does he respect and value your thoughts and opinions as equal to his own? Does he seek your input in decisions, or make them himself and just expect you to follow? Can you have conversations with him about your interests and desires, and does he take them seriously? From what you've told us it doesn't sound like the answer would be yes, but only you know the full story.
I know you're probably a bit shocked, but I hope you'll take this as an opportunity to look not just at the public groping issue, but your relationship as a whole. You deserve someone who loves you, cares for you, and treats you with the upmost respect. And know that if you do decide to leave, there's support for you on here and in real life too.