1. Mother either cooks something special for us or takes us to a restaurant at weekends.
2. Mother either cooks something special for us at weekends or takes us to a restaurant.
I'd like to know whether they mean the same. Thanks in advance.
Yes, they are fine and they mean the same. The only difference is in the ordering, in that the PP "at weekends" is in a different position in each example, but it does not change the meaning.