Is the first wife sinful for this action of hers, which may lead the second wife to seek a divorce? And is this considered incitement? And is the second wife sinful if she seeks a divorce for that reason?

It is permissible for a woman to suggest to her husband that he marry another woman, as long as her intention is righteous, because deeds are judged by intentions. However, if her intention is malicious, such as scheming against her co-wife, then that is forbidden. A wife is not entitled to waive the right of another woman to overnight stays and financial support. The husband must be just among his wives, even if they are in different countries. If the husband is just, the wife is not permitted to seek a divorce; but if he is not just, then she has the right to do so.