Elenore Roosevelt and Maria Callas both entertained ambassadors. But Maria Callas entertained them when they were watching her sing at the opera, Elenore Roosevelt entertained them by hosting social events which they attended.
So the word means two different things, depending on the context. That's why there are two different definitions.
You can also just say that Elenore Roosevelt entertained frequently. Since it doesn't say she entertained anyone in particular, you assume that the first meaning, that of hosting a social event, is meant. If you say "Bob entertained Kate", it's more likely that you mean he amused her, not that he hosted a party, but if you said "Bob entertained the prince of Monaco", you probably meant that he threw a formal event that the prince attended. You'd need context to be sure.
So for what it's worth, I'm going to disagree a bit with your definition 1, I don't think it's 100% correct. I'd say that the wealthy woman throwing a social event is "entertaining", but it's about her hosting a social function, the food and drink is incidental.
"Wining and Dining" is about wanting a favor from someone, or at least wanting to impress them, so you spend money showing them a good time. Keeping them amused is part of this, so I'd say the person 'entertaining' another person is primarily amusing them, not primarily hosting a social function, even though they might be doing that too.