American wife/British husband and legal rights

Hello.

I am hoping someone can help to answer my question regarding emergency situations and spousal rights. If an American female citizen (living in England for 4 years with indefinite leave to remain) is married to a British male citizen and has children; if the husband/father dies, what rights does the American female citizen have assuming no will has been assigned as the children are both under the age of two years? Does the wife lose all rights to the family finances and do they go to the government? Or is she protected under the UK or USA law to the family's finances?
Obviously a will is necessary but in the meantime.....

Thank you.

Any reason why you have not applied for Naturalisation as British?

As regards current ILR status, you obviously have the right to stay in the UK, with your British Citizen children.

No Will? Lots of places on the internet detail the intestacy rules. For example, thanks to a google search .... click here. Those are the UK's rules. US rules? Haven't got a clue what they are, or whether they would apply.

The citizenship of the surviving spouse is irrelevant for probate purposes.