Child: I am Papa's child. I am Mama's child.
Mama: Oh, so you are both of our child?
Both X or both of X means two/a pair of X together. There is one child, so both can't be used this way to refer to the child (keep reading, though).
There are two parents, which form a pair, so you want to use both referring to them. This is likely what you are looking for:
Mama: Oh, so you are the child of both of us?
or
Mama: Oh, so you are the child of us both?
Now, if the parents were responding to the child with a joke or sarcastic retort, then Mama might say:
Mama: Oh, so you are both of our children?
The plural of child is children and since both refers to two things what follows has to be a plural.
Do you know when the package is expected to be shipped?
When is the expected date for the package to be shipped?
Both of these are acceptable. The term you're looking for, I think, is passive voice since "is expected" and "to be shipped" are in the passive form of the verbs "to expect" and "to ship":
They expect that I will ship the package
It is expected (by them) that the package will be shipped (by me)
To answer your question about other ways to say this, the passive form of the verb sounds somewhat more polite than the active form. If you don't care about politeness, you can use the active voice:
Do you know when you expect to ship the package?
What is the expected date you will ship the package?
or even more direct:
When are you going to ship the package?
There are, of course, many other verbs you can use to express the same concept:
When do you plan to mail me the package?
When do you think you will deliver the package?
When do you anticipate the package will arrive?
And so on.
Final note: In your second sentence "expected" is not the past tense of "to expect". It's the adjective form of "expect" that modifies the noun "date": "the expected date"
Best Answer
To want one's bread buttered on both sides is a mainly British English idiom meaning to want to benefit or profit from two opposite or contradictory things, or to want to achieve or gain something without payment or effort, e.g. "Young people these days want their bread buttered on both sides - they want high paying jobs, but they aren't prepared to work for them!" A similar idiom is to want to "have one's cake and eat it". To have one's bread buttered on both sides is an unusual usage, and might well convey the implication that the success was not deserved, or achieved by unfair means, so I would use it with care. It might be acceptable if clearly meant humorously, and said to someone you know well.
Bread buttered on both sides