However, the southern part of Ireland was unwilling and broke away to form its own government. So only Northern Ireland joined with England, Wales and Scotland to become the United Kingdom and this was shown to the world in a new flag called the Union Jack.

本句，不定式作“结果状语”。

不定式作 “结果状语”， 还是“目的状语”，只有一步之遥。做到了就是“结果”，尚未做到就是“目的”。对比如下：

Dublin has rocketed up the charts to become one of Europe's most popular tourist destinations for city breaks. （结果）

都柏林的排名飞速攀升，成为了欧洲最受欢迎的旅游度假城市之一。

《柯林斯高阶英汉双解学习词典》

Sometimes adversity is what you need to face to become successful.（目的） 

逆境有时是你达成成功所必需经历的。

不定式无论作目的状语还是结果状语，其逻辑主语都应该是句子的主语。可是本句中句子的主语为Northern Ireland，不定式为to become the United Kingdom, 不定式的逻辑主语显然不是句子的主语。我猜想这是网友问题所在。

从逻辑上讲，不定式的逻辑主语应该是Northern Ireland，England, Wales and Scotland，所以，我认为目前这个句子的不定式结构在语法上是有问题的，需要修改，可以作如下修改：

1 So only Northern Ireland joined with England, Wales and Scotland and together they formed the United Kingdom. This was shown to the world in a new flag called the Union Jack.

2 So only Northern Ireland joined with England, Wales and Scotland to become part of the United Kingdom and this was shown to the world in a new flag called the Union Jack.