1) If my husband refuses for his share in the whole investment or property that my mother-in-law has can I claim it? Because ideally, my kids have right to the ancestral property.
It is not ancestral property to your kids hence on any basis you cannot claim any right in it.
It is your mother ion law's own and absolute property, in which even your own husband cannot claim any share as a right.
If your mother in law wants to give this property besides other movable property to her daughters alone, nobody can stop her from doing so, at least legally.
Further you cannot stop your husband from taking care of his mother even if she is not giving him anything in return, it is his duty to take care of her as per law.
If he has derelicted his duty to you and your children then you can claim maintenance from him
Fancies and whims do not find place in law.
2) Can I demand to know what all investment she has as they all (my husband his mother and sisters) are keeping me away from it?
No, you do not have any right to know any personal details about not only your mother in law but also about your own husband.
There is no provision in law for that.