Praise be to Allah.
It is permissible for a traveller to break the fast in Ramadaan, because Allaah says (interpretation of the meaning):
“So whoever of you sights (the crescent on the first night of) the month (of Ramadan i.e. is present at his home), he must observe Sawm (fasts) that month, and whoever is ill or on a journey, the same number [of days which one did not observe Sawm (fasts) must be made up] from other days. Allaah intends for you ease, and He does not want to make things difficult for you”
It makes no difference whether the travel is difficult or easy.
But is it better for him to fast or not to fast?
The answer is that it is better for him to fast, unless he experiences difficulty in which case it is better for him not to fast.
It is better for you to go back to your family and stay with them in order to help your wife with the housework and help her to do acts of worship and to benefit from the last ten days. Your staying with your family to encourage them to worship is better than your observing i’tikaaf on your own and depriving them of that help because of your being far away from them. ‘Aa’ishah (may Allaah be pleased with her) told us about what the Prophet (peace and blessings of Allaah be upon him) used to do during the last ten days, which included waking up his family – i.e., so that they could worship, pray and say du’aa’. The Prophet (peace and blessings of Allaah be upon him) did not observe i’tikaaf and leave his family with no help or care. It is proven that Safiyyah (may Allaah be pleased with her) visited him when he was in i’tikaaf and it is proven that they observed i’tikaaf with him. I’tikaaf is a private act of worship that does not benefit anyone else. Your staying with your family and encouraging them to worship and treating them kindly is an action that benefits others and you will not be deprived of the reward for their worship and you will not deprive yourself of worship, because you can accompany your family to qiyaam al-layl (night prayers) in a mosque, and you can wake them up at the end of the night to say du’aa’ and read Qur’aan. This is something good that will include you and your family. So we advise you to go back to your family and stay with them during the last ten days, and encourage them to worship Allaah. If you think that your family are doing well, and that they are performing acts of worship regularly, then you can observe i’tikaaf on some nights in your local mosque, so you can combine different kinds of worship and attain a great reward in sha Allaah. We ask Allaah to help you to do that which He loves and which pleases Him, and to accept the good deeds from you and your family.
And Allaah knows best.