It is a tough one, even though we could figure out what "the oth

And this is my humble opinion, for your reference only. 

个人拙见，仅供参考。

My first understanding is derived from Mr.and Mrs.Browning's background: the spiritual influence on their work. The link of Wikipedia reveals that "Much of Barrett Browning’s work carries a religious theme" and "She believed that Christ's religion is essentially poetry—poetry glorified. She explored the religious aspect in many of her poems, especially in her early work, such as the sonnets."So was her hu*****and, Mr.Browning. You can sense some hint from his work as well. 

If you think the above reasoning is way too farfetched, then lets return to the general cultural background. "The other world" has always been an allusion (an overtone) of "paradise" in the occidental world. Because "love" is emphasized in the quotation, so it won't be "hell" for sure. 

Then, "the other world" could be paradise, heaven, kingdom of God.........there're many many names of this paradise, where we'll become eternal. 

But love is forever eternal, this world or the other world. The western culture believes that love is the powerful force that keeps us alive,even after death. 

剩下的怎么翻译就看你了，直译“另一个世界”还是按照历来的习惯译。

不过这真是个beautiful piece......I've also heard that the book fell from the shelf on its own~~很美的故事，可惜，他们在一起生活的日子还是短了些。小时候看过童话Pied Piper of Hamelin，后来才知道这是Robert Browning从民间童话故事中采集来的，呵呵～

Have a good night!