The children should never be made to suffer. They're blameless. Yes, in some situations they're used as pawns between the parents and even the state, but if there's none of that going and the father just can't be bothered to maintain a relationship with the kid, then that's just not on. A child needs a father.
The Khalsa Panchayat - the Sikh Council of army chiefs threatened to kill Raja Lal Singh over this affair.
Sher Singh was very admiring of the British and their war technology. Being a natural and gifted soldier this was natural.
This is a common theme in royal households. Queens wanting their son to be King so it would raise their own profile prestige and power.
Think about this. Maharaja Ranjit singh committed some kurehit. Akali Phoola Singh had him tied to a tree, ready to be whipped. Why didn't Akali Phoola Singh claim the throne of Lahore?
The Dal Khalsa did crumble. After makng many victories and taking rule of large swathes of territory what happened to the Dal Khalsa within a decade ? They all starting fighting each other and became weak.
Just an old wives tale.