Is 交替更迭 redundant? Would this be proper grammar: 雨天與晴天交替?
交替 and 更迭 are two similar terms that complement each other in an four characters idiomatic phrase. Using four characters idiomatic phrase is a very common practice in Chinese speech. 

For example:

小心 (careful) and 謹慎 (cautious) have similar meaning, it is often put together as an idiomatic phrase (but not a true idiom)

You can say "你要小心" or "你要謹慎", they deliver a similar message, and both are to the point. 

You can also combine the two adjectives into one idiomatic phrase "小心謹慎" and say "你要小心謹慎" to illustrate a more detailed message and add literary flair to your speech.  

"雨天與晴天交替更迭" is grammatically correct and detailed. However, it would be more elegant to say "晴雨交替" or "晴雨更迭" (another way to make idiomatic phrase is reduce a long phrase into four characters phrase)

More examples:

縱横 (intersecting) 交錯 (crossing) --> 縱横交錯

聰明 (intelligent) 伶俐 (smart)  --> 聰明伶俐

We do it in English too, e.g. "He is a clever, smart man"