I remember mentioning how the Maratha, Ahom and Mysore taking care of the Mughal Siblings when they were born around 1820-1850 AD but the problem I am aware of is the fact these empires had fallen right before or after the Mughal Siblings were born so how should they be alive?

Refresher!
Maratha Empire ended in 1815
Ahom Dynasty ended in 1826
Kingdom of Mysore ended in 1947 but it was taken over by the British in 1831

India was born in 1827
Pakistan was born in 1832
B.A. (he was known as Mughal Army at the time) and Bangladesh were born in 1845

Here's my short explanation of my AU:

∙ When an empire or country's time has ended it doesn't mean the CH will die right away since it will only depend on their will if they want to die alongside their fallen empire but it will depend on their physical state and health

∙ This explains why Maratha, Ahom and Mysore will be alive but their empires wouldn't

∙ Maratha was the first to fall but he didn't and instead had taken refuge in the Mughal Empire in 1815

∙ Ahom was the second to fall in 1826 but he took took refuge in the Mughal Empire

∙ Mysore hadn't collapsed but it was taken over by the British so she fled to the Mughal Empire in 1831

∙ Maratha, Ahom and Mysore were finally killed around 1858 after the Mughal Empire was slaughtered but Mysore's kingdom continued on till 1947 thanks to the British

∙ Koch Bihar could have lived after her Dynasty fell but her physical state was weakened so she had to collapse alongside her dynasty 

∙ Koch Hajo was slaughtered along with his land so he wasn't able to live until how much he could

∙ Mughal Empire was also slaughtered along with his empire falling thanks to the British Empire at around 1858 and that was the same time British India/British Raj replaced the Empire

∙ To clear any confusion, India, Pakistan, B.A. and Bangladesh make up the British Raj with India being the one to take the lead while her siblings were either neglected, locked away or tortured

∙ B.A. and Bangladesh were only 13 with India being 31 and Pakistan being 26 when their father, the Mughal Empire ended

∙ Their flag instantly shifted when the Mughal Empire ended and it is the same when India and Pakistan became independent whereas B.A. and Bangladesh were under Pakistan's rule before they became independent and their flags changed too

Hope this was helpful and made sense! ^^;;