The Gate of Kelves is Chapter 3 of Fire Emblem: Thracia 776.
The most important thing to focus on in this chapter is returning all of the children to their homes. A child's name can be seen by checking their stats page. If your instance of the game is untranslated (or you do not understand Japanese), the order of the children in their starting positions, from left to right, are Yubel, Romeo, Coirpre and Lucia. Romeo goes to the upper left house, Coirpre to the upper right, Lucia to the lower left, and Yuvel to the lower right. Returning Romeo and Lucia will grant a Shield Ring and the Baldr Scroll respectively. The other two will yield nothing immediately but are still incredibly important. Returning Yuvel will allow you to recruit Dalsin in the next chapter and Coirpre will get you a Warp in Chapter 7.
Luckily, saving the children is not particularly difficult. The main thing to watch out for is the barbarians who will spawn from the western forest and attempt to destroy the houses around Turn 10. Two will spawn each turn for seven turns. Eyvel and other sword-wielding units should have little trouble dispatching them if they are in place when the barbarians arrive. It is also a good opportunity to give EXP to Leif or Lifis. Also, watch out for the Sword Armor Knights and Soldiers that will spawn next to the boss around Turn 12. Once they, and the enemies surrounding the children, have been killed or captured, there will be no danger while rescuing the children and bringing them to their respective homes.
The two chests in the upper part of the map contain an Armor Slayer (left) and a Meteor tome (right). The bishop in the back will use the door and chest keys in his inventory to take the Meteor tome out of the chest behind him around Turn 10 and begin using on units in his range. As such, it would be ideal to capture him before he has a chance to do so. With the newly acquired Armor Slayer and Dagdar's Hammer in tow, the boss should be simple.
After defeating the enemies, it is a good idea to use the Supply Convoy in the upper-right corner to deposit the extra weapons clogging up your inventory. Similarly, the Shop in the upper-left provides a location to sell unneeded items. The shop also sells door keys, which you will want to start stocking up on now as they are helpful throughout the game and essential in the final chapters.
Before seizing the throne, give all important items to Leif and Lifis because, of your current party, only these two will be usable for the next five chapters. The highest priority should be the two Crusader Scrolls and all of the swords you currently have. The coming chapters will not have very many to take from enemies. The only ones available are Longswords from the difficult to capture Sword Armor Knights. Furthermore, most units you control will exclusively use them during the first three indoor chapters. Vulneraries are also helpful but can be relatively easily stolen from the Soldiers in the next chapter, so only one or two are necessary. This is also Eyvel's last chapter under player control for the majority of the game, so be sure to transfer her better items, such as her Flame Sword or a Crusader Scroll, to storage or another unit.