He has two houses in different cities; can he shorten his prayers when he goes to one of them, or must he offer the prayers in full?
Question

I have a house in a coastal city 300 kilometres from my house, which I visit sometimes on the weekend for three days, from Thursday to Saturday. What is the ruling on shortening my prayers in this case? Is it valid for me to pray Zuhr instead of Jumu‘ah?
Praise be to Allah.If someone travels the distance at which it becomes permissible to shorten the prayers, which is 85 kilometres, it is permissible for him to shorten prayers and put them together during his journey, then when he reaches his destination, the matter is subject to further discussion:
1.. If that is his place of permanent residence, then he must offer the prayers in full and not shorten them.
2.. If it is not his place of permanent residence, even if he has a house or relatives there, but he does not reside there, then if he intends to stay for more than four days, he should offer the prayers in full, but if he intends to stay for a shorter time than that, he may shorten the prayers.
Imam ash-Shaafa‘i (may Allah have mercy on him) said: If he comes to the city, and he has relatives or in-laws or a wife in any part of the city, but he does not intend to stay there for four days, then he may shorten the prayers if he wishes. The companions of the Messenger of Allah (blessings and peace of Allah be upon him) shortened the prayers with him at the time of the conquest of Makkah, when he did Hajj, and when Abu Bakr led the Hajj, even though many of them had one or more houses in Makkah, and they had relatives there. They included Abu Bakr, who had a house and relatives in Makkah; ‘Umar, who had many houses in Makkah; and ‘Uthmaan, who had a house and relatives in Makkah. But I do not know that the Messenger of Allah (blessings and peace of Allah be upon him) instructed any of them to offer the prayers in full. He did not offer the prayers in full and neither did they, after the Messenger of Allah (blessings and peace of Allah be upon him) passed away, when they came to Makkah." (Al-Umm 1/217).
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: I am someone who lives in al-Qasim, and sometimes I go to Riyadh to visit my family, as I have a room there, and I stay with them for two or three days. Am I allowed to shorten my prayers when I pray on my own? Do I come under the same ruling as the traveller?
He (may Allah have mercy on him) said: Yes, you come under the same ruling as the traveller, because your homeland is al-Qasim, and when you visit your family you visit as a traveller. Hence the Prophet (blessings and peace of Allah be upon him) shortened his prayers in Makkah, even though he had previously been a resident of the city and he had houses there, but when he migrated, Madinah became his homeland. Therefore when you go to your family, you are a traveller." (Liqa’ al-Baab al-Maftooh  58/23).
It says in Fataawa al-Lajnah ad-Daa’imah (8/147):
Question: What is the ruling on shortening prayers, if someone has two houses in two different cities in the same region, and he resides in both, and travels from time to time? If he travels to one of them, does he have to shorten his prayers or is it permissible for him to offer them in full? We would like a clear explanation about shortening prayers in general.
Answer: If the situation is as described, that he has taken both houses as places of residence, then it is not permissible for him to avail himself of the concessions of travel, such as shortening prayers and so on, when he is residing in either of the two cities. But he may avail himself of those concessions whilst he is travelling between the two cities, if the distance between them is the distance at which it becomes permissible to shorten prayers, which is approximately eighty kilometres.
‘Abdullah ibn Ghadyaan, ‘Abdullah ibn Ghadyaan, ‘Abd ar-Razzaaq ‘Ajeefi, ‘Abd al-‘Azeez ibn ‘Abdillah ibn Baz. End quote.
As appears to be the case from your question, this house in the coastal city is not your place of residence, so when you stay there, you may shorten your prayers, so long as you do not intend to stay there for more than four days, in which case you must offer your prayers in full.
And Allah knows best.