I partially disagree with the two other answers (as of the time of this writing).
The Don't.
Let's use a slightly different example sentence to make the nuances clearer:
My classmates don't follow the rules.
This means that the classmates have a general habit of not following the rules. It's form of time-agnostic knowledge; it's possible that you're now attending another school and talking about ex-classmates.
The Won't.
My classmates won't follow the rules.
This suggests that there exists effort directed towards making the classmates follow rules. The phrasing gives an implication that there's an opposing force that's trying to behave your classmates.
Your example.
They don't let you smoke in here.
This is general; the speaker has probably deduced that from a no-smoking sign or similar.
They won't let you smoke in here.
This would imply that the speaker has probably actually tried to smoke once and they didn't let him. You might end up getting the implication that he tried to convince them ('oh, just this one cigarette'), which is the effort we mentioned in our conceptualization.
Note: this is a pretty small and nuanced difference; nobody will get confused if you use them interchangeably, but it does come quite naturally for native speakers.
Lastly: the In.
Simple:
It was getting crazy and hot in here.
This is localized; it was probably getting crazy in a room, hall, or some other enclosed 'cozy' place.
It was getting violent here.
This is more general and can refer to any type of place that is more likely abstractly-bordered-and-contained than having brick-and-mortar walls; think countries and nations, school campuses, streets, etc.
Is "assist in" the same as "assist with"? Can I always substitute the one where the other is used, or is there a difference in meaning?
In general, they're pretty similar and frequently interchangeable -- at least one-way. (You can say "assist with" for "assist in," but you should be careful swapping "assist in" for "assist with," since there are some nuances.
If you "assist in," it may indicate a longer-term and/or more in-depth assistance -- the senior academic meeting with the junior one daily over a course of months, for instance.
If you "assist with" something, it can indicate a much shorter-term, or "shallower" form of assistance -- you aren't going around asking questions to help the police, but are instead answering the questions the police gave. (If you said "I am assisting in the police inquiries," you would be presumed to be doing a share of the work.)
So you can assist your co-worker with a project, or you can assist your co-worker in his work, and it means pretty much the same thing. (Though even there, notice the nuance: a project is a thing with an end, while "his work" is more open-ended!) But you want to be careful saying you're assisting the police in their investigations unless you mean that you're doing more than just answering a few questions.
However, even if you use the "wrong" in/with, a sentence in context will usually be interpreted the correct way.
Best Answer
In English, "have" is a very flexible word that can be used in a variety of contexts. I can have freckles on my face, I can have cake for dessert, and I can have a dead battery in my car. Furthermore, we can have parties, conversations, naps, arguments, elections, and children.
Getting back to your question, we can also have a taste of the soup.
There's only a small difference in meaning between "let my sister taste it," and "had my sister taste it," although "let" carries a connotation of allow or permit, while "had" might imply a little insistence on your part. In other words, had she asked for a taste, and you said yes, then "let" might be a better word to use. However, if you weren't sure the soup tasted satisfactory, so you wanted your sister to give a second opinion, then "had" might be a better word.
Incidentally, yet another way to word this would be:
which combines both of those words, and would sound perfectly natural to a native speaker.