Is it difficult to connect with some of the emotions during some of the dances?

Yes, and it's not something I have down in Latin yet.

Standard/smooth I'm fine with. Latin/rhythm... not so much.

Yes! Especially when you feel the overwhelming urge to laugh at your partner while your trying to display serious emotion! Much like acting - you have to find it within you - somewhere - and connect to the dance/music. (-:

It is difficult. As Days said, it is very much like acting.
I feel that there are different difficulties based on the setting. At a social dance, the main difficulty I always feel is that the random partners you are dancing with will allhave their own level of involvment with dancing and might be confused by your dance emotions.
If you have a set partner you compede with, do showcases etc, then I believe it is something the two of you will have to work on together. It will be easier since you will be doing the acting with someone you can be comfortable with, it will have the added difficulty though that you will have to work together - you might be showing the waltz emotion perfectly based on your interpretation, if your partner's interpretation is different though, even though both of you on your own would be amazing, as a couple...
It's dancing, you are never in it alone ;)
That's my take anyway