This is kind of a fuzzy, gray area for many mormons. Active, practicing mormons - as you know do not drink alcohol. But when it comes to cooking with alcohol there are not as clear definitions about that - and it comes more down to the individual. For example, I really like Chicken Marsala at Olive Garden because I feel that the alcohol for all intents and purposes has been cooked out. (There is some debate about the actual facts around that though.) However, my daughter will not order/eat chicken marsala because it makes her feel uncomfortable which I respect. Some practicing mormons do cook with wine, but most would not do it. For desserts with liquor in - I think most practicing mormons would not eat it. 
 
In summary - there are some practicing mormons that would be ok with what you describe, but there are a high percentage of them that would be uncomfortable with it. 
 
I would encourage you to just ask them. It's not an embarrassing question for mormons to answer and they would appreciate being able to answer the question beforehand rather than having to answer and explain when they are about to eat. Some mormons would definitely not eat some of those things if they knew it contained alcohol. Just ask them. 
 
Hope that helps.

My husband and I have been invited into a Mormon household for dinner. Is it proper for us to bring a bottle of wine?

If I were invited to a friends house and they wanted to have wine - I wouldn't have a problem with it and respect their wishes given it was their home. 
 
However, if I invited someone to my house for dinner and they brought wine with them to drink - I think it would bother me some given that it was my home. I'm not sure what other mormons would feel, but I would prefer not to serve wine in my home even though someone else brought it. Again I think it goes along with respecting the beliefs of the person whose home it is. 
 
Now I'll be a little hypocritical though. When it comes to coffee - my grandma (who was not a mormon) used to drink coffee and we would keep a little for her in our house. So I realize I'm not being consistent, but that's how I would feel. 
 
When it comes to smoking in my house - absolutely not. If someone wants to smoke at my house - they can go outside.

I have been invited to dinner at a Mormon home. It will be casual outdoor grilling. What should I bring as an offering?

I've been over to many other Mormons for dinner, etc. But bringing an offering is not really a thing that is expected. I know for others - bringing a bottle of wine or other gift is the norm, but for mormons I don't see that very much. 
 
Usually what happens is that we ask what can we bring - like a salad, dessert, etc. That is appreciated, but still not necessarily expected.