The description provided in the question, particularly the extreme irritability, quarrelsome nature even with loved ones ("bread and butter"), restlessness ("never at peace"), and being full of imaginations and fears, strongly points towards the homeopathic remedy Kali carbonicum (Potassium carbonate).
Dr. James Tyler Kent, a prominent figure in homeopathy, described the *Kali carbonicum* patient as being difficult to study due to their complex and often contradictory nature. Their irritability can be extreme, leading to quarrelsomeness with family members and those closest to them. They often experience marked inner restlessness, anxiety, and a tendency towards numerous fears and vivid imaginations.
Let's briefly consider why the other options are less likely to fit this specific description according to Dr. Kent's Materia Medica:
Lycopodium clavatum: While *Lycopodium* patients can be irritable and have fears, their irritability is often more about being contradicted or their authority being questioned. They also have a strong desire for company and support, which contrasts with the extreme quarrelsomeness described.
Opium: *Opium* is more associated with states of drowsiness, stupor, and insensitivity to pain, often following fright or shock. The irritability and mental restlessness described are not typical *Opium* characteristics in this context.
Nux Vomica: *Nux Vomica* patients are indeed irritable, easily offended, and can be quarrelsome, especially when contradicted. They are often ambitious, driven, and suffer from digestive issues. While there is some overlap, the extreme level of quarrelsomeness even with their "bread and butter" and the specific sense of inner restlessness and fear described by Kent are more characteristic of *Kali carbonicum*.
Therefore, based on Dr. Kent's description of the remedy and the patient's mental-emotional state, *Kali carbonicum* is the most likely answer.