Learn Swedish: Kanske vi kan adoptera ett husdjur.

You are right that Swedish is usually strictly V2! However, kanske is a famous exception. When kanske starts a main clause, it is very common to use V3 word order, placing the subject (vi) before the verb (kan). This happens because kanske originally comes from the phrase kan ske (it can happen), so it is historically treated almost like its own introductory clause.

Would it be grammatically wrong to use V2 word order and say Kanske kan vi adoptera ett husdjur?

Not at all! Both V3 (Kanske vi kan...) and V2 (Kanske kan vi...) are correct when starting a sentence with kanske. The V3 version shown in this sentence is extremely common in spoken and everyday Swedish, while the V2 version tends to sound a bit more formal.

If I move kanske to the middle of the sentence, does it still cause a word order exception?

No, if you do not start the sentence with it, standard rules apply. It behaves like a normal sentence adverb (like inte or ofta) and goes after the first verb in a main clause: Vi kan kanske adoptera ett husdjur. The V3 exception only happens when kanske is in the very first position.

Is husdjur used for any kind of domestic animal, like cows or pigs?