I've seen many issue arise depending on one's belief. If you are traditional, and the divorce was official (in the fact that they have sorted it out with both sides and the wife's side has called her spirit back with their clan), then her family is responsible for her funeral. If they separated, but her side of the family did not correctly call her spirit back with her clan, her clan may forbid her family from taking care of the funeral because that may bring bad luck to the clan. In which case, her clan will believe that her ex-husband's side must bare the responsibiliti es.
If she is a Christian and attends church regularly, her church will bare the responsibility . But if she is not a regular and is not active, they may not help.
If you want it done traditionally and neither party wants to help, I have seen people hire professional/experts come help them with the funeral (usually done by the children). Or if she is truly a Christian but just never went, just throw a simple quick christian funeral (again, usually done by the children).