Is it permissible for a divorced woman with children to have her son act as her guardian in the marriage contract if her father refuses to do so for illegitimate reasons, such as being a polygamist?

A guardian does not have the right to prevent a woman from marrying someone she wishes to marry merely because he has been married before. If the guardian refuses to marry her off without a legitimate Shar'i (Islamic legal) excuse, then he is hindering her marriage, and the guardianship transfers to the next closest guardian or to the judge. It is advisable to try and convince the guardian to agree to the marriage. Otherwise, the matter should be referred to the Shar'i judge to consider it and either marry her off or instruct her next closest guardian to do so.