unless is not always an alternative to IF NOT.
In my grammar book, it is said UNLESS is not always an alternative to IF NOT especially when the negative connotation after IF is contrary to known facts .

You'd be happier unless you had such high expecations.

What time shall we leave for the theatre unless he turns up.

These are marked as incorrect.

Not very sure about the first sentence. Why we can't use unless?

Question

unless is not always an alternative to IF NOT.
In my grammar book, it is said UNLESS is not always an alternative to IF NOT especially when the negative connotation after IF is contrary to known facts .

You'd be happier unless you had such high expecations.

What time shall we leave for the theatre unless he turns up.

These are marked as incorrect.

Not very sure about the first sentence. Why we can't use unless?

Answer

Look at this sentence:

You can’t come in unless you have a membership card.
This sentence means “the only way for you to come in is to have a card.”
Unless is not simply “if not”. It kinda means “only if”

Or this one: your new credit card won’t work unless you validate it through your bank profile.

Which means when you receive your new credit card, it won’t be operative immediately; the only way to get it to work is to go to your profile and finish the validation procedure.

In your examples you should use:

You’d be happier if you didn’t have such high expectations.
Your second example makes little sense to me... could you explain it better?

Answer

The   first one  is type 2  conditional so I'd re-write it like : 
you would be happier if you had such high expectations.  (  Although this  sentence sounds kinda weird in terms of conceptual meaning    .. it  must be:  if you didn't have    )

"Unless "  doesn't make sense here.

you use  "  Unless  "  to make a simple exception.

for example:  
I'm NOT gonna give you the password unless  you give me yours 
I'm NOT gonna give you my password if you don't give me yours.