Is a wife obligated to serve her husband's children from another wife, and do the angels curse the one who refuses to serve them and whose husband becomes angry, and is that considered a dereliction of her husband's rights?

The wife is not obligated to serve her husband's children from another wife, nor to serve his relatives. The husband does not have the right to force her to do so. However, if she does so out of kindness, she will be rewarded. If the wife refuses and the husband becomes angry, it does not harm her if she was not the one who initiated the abandonment or injustice.