Is it permissible for a woman to marry without a guardian (wali) in his absence, especially if she was previously married and has children, and is it valid for her aunt's husband to be her guardian in the marriage contract?

Marriage is not valid except with a guardian (wali). A woman does not have the right to marry herself or others, nor can she appoint someone other than her guardian, regardless of whether she has been married before or not, and whether she is young or old. This is based on the Almighty's saying: (And marry the unmarried among you), and the Prophet's (peace be upon him) saying: "There is no marriage without a guardian," and "Any woman who marries without the permission of her guardian, her marriage is void." The most entitled person to give a woman in marriage is her father, then his father no matter how far up, then her son then his son no matter how far down, then her full brother, then her half-brother (from the father's side), then her nephews, then her full paternal uncle, then her half-paternal uncle (from the father's side). If none of these guardians are available, the ruler (qadi/judge) marries her, based on the Prophet's (peace be upon him) saying: "The ruler is the guardian of whoever has no guardian." The maternal aunt's husband is not among the guardians.