Before the end of this day, when we would arrive in Barcelona, I wouldn't have to put up with anything anymore in the great Third Reich. 

1. when we would arrive in Barcelona：是非限制性定语从句，修饰时间the end of this day。因为，该从句即便去掉，句子仍然成立：

Before the end of this day, I wouldn't have to put up with anything anymore in the great Third Reich. 

2. this day 翻译成“今天”；

3. when 在这里翻译成“此时，这时”；

4. would 表示“可能性推测”，理解为“过去将来”也可。句子意思是：在今天结束之前，我们可能会抵达巴塞罗那。