Rights of widow in her ex-inlaws property after her remarria

No. The property owned by your ex mother-in-law becomes her absolute property. She is not legally bound to give the property either to you or to your kids. She is entitled to give it to any one of her choice.

How did your ex-MIL became owner of the house i.e., it is her self acquired or inherited by succession?

If it is inherited all 3 of you have a share which can be claimed.

Who are her other legal heirs?  Have you contacted her and requested to take care of the future of her own grandchildren who are father less ?  If it is an arranged marriage, what are the possibilities of convincing her for bequeating her property through a registered will through the intervention of relatives and friends that can convince her ?  Do not go for litigation and it should be the final step if there is no alternative remedy.

The house which my mother in law is the owner of was given to her by her husband by mentioning in his will

As presumed, the house is her absolute property, if your father in law has acquired the house with his self acquired income.  Prevail over her by maintaining good relations and send grandchildren to her house frequently and let the relations be not broken, as grandmother must be having soft corner to her GC as her son is no more.

My kids are living with me and my husband after the arranged marriage that I had post my ex husband's demise.

Talking about exM hiers, she has a daughter , widowed daughter in law and her kids staying with her

Your children continue to be the legal heirs to the ex-mother-in-law. They are entitled to succeed a share in her property left intestate.