Is it permissible to transport a funeral from the capital to the village to bury it there, and is it permissible to bury the deceased with their relatives?

Transferring the deceased from one country to another before burial is a matter of scholarly disagreement:

Malikis: They permit transferring the deceased if their sanctity is not violated and they are not harmed, citing the transfer of Sa'id ibn Zayd and Sa'd ibn Abi Waqqas as evidence. Hanbalis: They dislike transferring the deceased without need, stipulating that the body must not decompose, except for a valid purpose such as a noble location. Hanafis: They dislike transferring the deceased for a distance greater than two miles, as it is an engagement in something unfruitful and delays the burial. Shafi'is: They have two opinions: prohibition due to dislike, unless it is near Mecca, Medina, or Jerusalem.

It is permissible to bury the deceased with their relatives if their sanctity is not violated or they are not harmed. However, it is preferable not to transfer the deceased from the town where they passed away, to avoid scholarly disagreement and to prevent delaying their burial.