Does she have to uphold ties of kinship with her husband’s relatives even after divorce?

Upholding ties of kinship only has to do with relatives through one’s father and mother, not relatives through marriage. 

Shaykh Ibn Baaz (may Allah have mercy on him) was asked: 

I hope you can advise me in detail about upholding ties of kinship. Does it include the relatives of one's wife or husband or not? Who are the arham (close relatives)? 

He replied: 

The arham are relatives through one's mother and through one's father. So fathers, mothers, grandfathers and grandmothers are arham. And one’s children and their children, both male and female, and the children of daughters, are all arham. Similarly, brothers and sisters and their children are arham; and paternal uncles and aunts, and maternal uncles and aunts, and their children are arham. As for the relatives of one's wife, they are in-laws or relatives through marriage, and they are not arham. The same applies to the husband’s relatives for the wife – they are relatives through marriage and they are not arham. 

End quote from the Shaykh’s website. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

Many of the common folk take the word arham as referring only to the relatives of the spouse, to such an extent that a man may say these are my arham because he is married to one of them. This is a mistake in both linguistic and shar ‘i terms, because the arham are relatives through one’s father or through one’s mother. 

As for the relatives of one’s spouse, they are called as-haar (in-laws), not arham. Allah, may He be exalted, says (interpretation of the meaning): “And it is He Who has created man from water, and has appointed for him kindred by blood (nasaban), and kindred by marriage (sihran)” [al-Furqaan 25:54]. Allah, may He be exalted, has created ties among people by means of these two things: kindred by blood and kindred by marriage. End quote. 

Fataawa Noor ‘ala al-Darb by Ibn ‘Uthaymeen, 11/6. 

But that does not mean that there should not be good interactions among people, with ties, friendship and visits, even if there are no ties of blood or marriage among them. 

So there is nothing wrong with continuing good relationships among people who were related by marriage, even after divorce, this in fact is part of a good attitude and good character, because the Muslims is the brother of his fellow Muslim. 

But it is essential to point out the importance of adhering to proper shar‘i hijaab in front of adolescent male children. It says in al-Mawsoo‘ah al-Fiqhiyyah (17/7): 

It is obligatory on the woman to observe hijab in front of adolescents who can tell what is ‘awrah and what is not. This is a general rule. If the child is a minor and cannot tell what is ‘awrah and what is not, then there is nothing wrong with showing one’s adornment in front of him, because Allah, may He be exalted, says (interpretation of the meaning): “and not to reveal their adornment except to their husbands, …, or small children who have no sense of the feminine sex.” [al-Noor 24:31]. 

End quote. 

The boy in front of whom hijab does not have to be observed is the one who has no knowledge of or interest in matters having to do with women. This varies from one child to another. End quote. 

Fataawa Noor ‘ala al-Darb by Ibn ‘Uthaymeen, 11/500 

And Allah knows best.