Is it obligatory to divorce the second wife, or to continue with her and face the problems resulting from that, given the questioner's desire not to divorce her and his love for the first wife?

If you know yourself to be weak in handling polygyny, then it is better to abandon it. Preserving the stability of your current marital life with the mother of your children is more important than entering into another unstable life. However, if you are in need of a second wife and are able to be just, then it is better to keep the first wife and resolve disputes wisely. You should perform Istikhara (prayer for guidance) and consult those with experience.