If you say '두 번만' , it means 'only twice (no more than twice)'. '만' is not repetitively used for different nouns in one sentence. If you want to also emphasize '두 번' at the same time, you can use '딱' before '두 번'. e.g. ) 일 년에 딱 두 번 운동만 해요.

Both of your sentences are correct, but I think the second one is more commonly heard. 만 can be attached to many parts of the sentence depending on what you want to say. Here is an example on a similar sentence: "일 년에 두 번 친구하고 운동해요 [or 운동을 해요]." (no special emphasis) 1. 일 년에 두 번만 친구하고 운동해요 = I only exercise twice a year, with my friend. ("only twice") 2. 일 년에 두 번 친구하고만 운동해요 = I only exercise with my friend, twice a year. ("only with my friend") 3. 일 년에 두 번 친구하고 운동만 해요 = Twice a year, I do nothing but exercise with my friend. ("only exercise") 4. 일 년에만 두 번 친구하고 운동해요 = Twice in just one year, I exercise with my friend. ("twice just in one yea"r) All are correct sentences (#4 is probably not the best way to say it though) emphasizing different parts.