Praise be to Allah.
As the mosque is far away, it is permissible for you to pray in your home, and to lead your family in prayer. Do as the Prophet (peace and blessings of Allaah be upon him) did, as described in the hadeeth narrated by Anas (may Allaah be pleased with him) and reported by al-Bukhaari and Muslim: “He said to them, ‘Get up and let him lead you in prayer.’ The Prophet (peace and blessings of Allaah be upon him) stood up, and the orphan and I formed a row behind him, and the old woman stood behind us. The Prophet (peace and blessings of Allaah be upon him) led us in a two-rak’ah prayer, then he left.”
Make your two children stand behind you in one row, and their mother can stand behind them. If their mother is not praying because of menstruation etc., then lead the two children in prayer, with them standing behind you in one row. It is OK if a boy who has reached the age of discretion recites the Iqaamah. The age of discretion is usually seven years or above. He can recite the Iqaamah so long as he understands the basic essentials of the prayer. And Allaah knows best.