Final answer:
The correct way to combine the sentences is: This summer, my family and I will visit our relatives in Uruguay; however, we will not visit our relatives in Peru. This uses a semicolon and a comma to combine the independent clauses appropriately.
Step-by-step explanation:
The correct way to combine the two sentences is by using a semicolon to separate the two independent clauses and a comma after the conjunctive adverb 'however'.
So, the correct combined sentence would be:
This summer, my family and I will visit our relatives in Uruguay; however, we will not visit our relatives in Peru.
This construction correctly uses both the semicolon and the comma as outlined in English grammar rules for combining independent clauses with conjunctions.