Thank you Jessie Fong for sharing the beautiful story on home funeral of Caroline Kirk.
I would think whether it is a home funeral handled by professional or own family member, it is important that the deceased is treated with respect, dignity and peace. There should not be a lot of crying or being emotional as it would cause the deceased to be attached to the samsara and do not want to move on for his/her rebirth.
For Buddhist, prayers such as Dorje Shugden Prayers, Medicine Buddha prayer, Lama Chopa, or reciting Amitabha mantra or Om Mani Padme Hung would be good. Dharma protector prayers such as DS prayer and mantra is important as protector would help to bring the deceased to a good rebirth so that the deceased will be closed to Dharma and able to practise Dharma for next lives.
On the other hand, it would be good to do their research beforehand and check out what are the necessary administrative processes to be carried out such as obtaining the death certificate for the deceased and filing for a disposition permit. Some countries may also have support groups or religious organisation that provide guidance on home funeral and how to handle the deceased body.