One can be at home and be in the backyard, that is, not in one's house at all.
Conclusion
Being at home is not required for being in your own house (i.e. it's possible to be in your own house, but not at home)
Evidence
You can be in your house but not at your home, if you own the house but rent it to others, for example. (That's your house. You own the deed. But you're just visiting your tenant. It's their home.)
Evaluate
On a first read, I would have certainly thought that each of the first two sentences were premises, but the first one is actually irrelevant.
The conclusion is a denying this conditional relationship: being in house ---requires---> being at home
In any context, when we're contradicting / negating / refuting a conditional statement, we're saying .
So in order for the author to prove that "being at home isn't required", she just has to produce an example where someone is in their house, but isn't at home.
The first sentence is about being at home, but not in your house. That's unrelated. That you would prove that .
Goal
We want to classify the role of the claim as either Main Conclusion, something Supporting, something Opposing, or something Neutral.
Since the conclusion is the last sentence and the support is the second sentence, we'll just call this first sentence Neutral.