Two tips: 1) It sometimes helps to rephrase the sentence into an equivalent English-sentence that looks easier to analyze. 2) Often times, you can break down the sentence to make it easier to parse. If you have trouble wrapping your head around the sentence, try phrasing it in a slightly more suggestive way. For instance:
"Every grandparent is such that either they have only daughters, or they have exactly two sons, or they have no children."
In general, "Every $\varphi$ is such that $\psi$" gets translated into the predicate calculus as $\forall x (\varphi(x) \rightarrow \psi(x))$. Your $\varphi(x)$ here is "$x$ is a grandparent", whereas your $\psi(x)$ is "$x$ either has... (etc.)". So overall, the translation should look like this:
$\forall x(x \text{ is a grandparent} \rightarrow x \text{ either has only daughters, or exactly two sons, or is childless})$
So if you can figure out how to say "$x$ is a grandparent" and "$x$ either has only daughters, or has exactly two sons, or is childless", then you'll know how to translate the sentence.
How do you say "$x$ is a grandparent"? Basically, it amounts to saying that $x$ has some child, who also has some (other) child. So this just amounts to $\exists y (C(y,x) \wedge \exists z(C(z,y)))$. This formula (which has $x$ free btw) is your $\varphi(x)$, which goes in the antecedent of the conditional of your universally quantified sentence.
How do you say "$x$ either has only daughters, or exactly two sons, or is childless"? Well, it seems to be a disjunction about $x$, so split it up into cases: if you know the whole thing is a disjunction, you can tackle each disjunct separately and then put it all together with $\vee$s at the end. So you just need to analyze "$x$ has only daughters", "$x$ has exactly two sons", and "$x$ is childless". Hopefully, things are clear enough that you can do these on your own.
You can take the word "nevertheless" as a clue indicating that what follows isn't implied by and clearly doesn't depend on, the preceding knowledge. "Nevertheless" could easily be replaced by the word "but" and still convey the same meaning, and as you know, we translate "but" as meaning "and":
"You get an A on the final, but you don't do every exercise in the book. But, you get an A in the class." This says pretty much what the original statement says.
If there were an implication (conditional) involved in the sequence of statements, you'd see something like "...Therefore, ..." or "As a consequence, ...".
So the correct translation here would indeed be $$(p \land \lnot q) \land r,\quad\text{or simply}\quad p \land \lnot q \land r$$
Best Answer
Hint:
I'd recommend you work inside-out. Here are a few to get started.
On the antecedent, we will ignore the universal quantifier: $$Person(x)\wedge \exists y(City(y)\wedge LivesIn(a,y)\wedge LivesIn(x,y)$$
Translates to
On the consequent side, we've got a lot going on. Let's go all the way in to
$$City(w)\wedge Likes(x,w)\rightarrow y=w$$
Note here that I've left $y$ unspecified since we haven't worked ourselves outwards enough to where we fix $y$.
Just go snippet by snippet like this. Leave the external quantifiers alone until you've figured out the inner parts.
Then you can put them together to get to a coherent English statement.