No, the husband of your younger sister couldn't be Mahram to you even if he is your father's sister's son. (Even if you travel along with them. (as far as I know). Then you ought to observe your Islamic code in front of him.
It could be beneficial for you to read the verse below (in regard to the persons who are Mahram to women):
وَقُل لِّلْمُؤْمِنَاتِ يَغْضُضْنَ مِنْ أَبْصَارِهِنَّ وَيَحْفَظْنَ
فُرُوجَهُنَّ وَلَا يُبْدِينَ زِينَتَهُنَّ إِلَّا مَا ظَهَرَ مِنْهَا ۖ
وَلْيَضْرِبْنَ بِخُمُرِهِنَّ عَلَىٰ جُيُوبِهِنَّ ۖ وَلَا يُبْدِينَ
زِينَتَهُنَّ إِلَّا لِبُعُولَتِهِنَّ أَوْ آبَائِهِنَّ أَوْ آبَاءِ
بُعُولَتِهِنَّ أَوْ أَبْنَائِهِنَّ أَوْ أَبْنَاءِ بُعُولَتِهِنَّ أَوْ
إِخْوَانِهِنَّ أَوْ بَنِي إِخْوَانِهِنَّ أَوْ بَنِي أَخَوَاتِهِنَّ
أَوْ نِسَائِهِنَّ أَوْ مَا مَلَكَتْ أَيْمَانُهُنَّ أَوِ التَّابِعِينَ
غَيْرِ أُولِي الْإِرْبَةِ مِنَ الرِّجَالِ أَوِ الطِّفْلِ الَّذِينَ
لَمْ يَظْهَرُوا عَلَىٰ عَوْرَاتِ النِّسَاءِ ۖ وَلَا يَضْرِبْنَ
بِأَرْجُلِهِنَّ لِيُعْلَمَ مَا يُخْفِينَ مِن زِينَتِهِنَّ ۚ وَتُوبُوا
إِلَى اللَّـهِ جَمِيعًا أَيُّهَ الْمُؤْمِنُونَ لَعَلَّكُمْ تُفْلِحُونَ
﴿٣١﴾
And tell the believing women to reduce [some] of their vision and
guard their private parts and not expose their adornment except that
which [necessarily] appears thereof and to wrap [a portion of] their
headcovers over their chests and not expose their adornment except to
their husbands, their fathers, their husbands' fathers, their sons,
their husbands' sons, their brothers, their brothers' sons, their
sisters' sons, their women, that which their right hands possess, or
those male attendants having no physical desire, or children who are
not yet aware of the private aspects of women. And let them not stamp
their feet to make known what they conceal of their adornment. And
turn to Allah in repentance, all of you, O believers, that you might
succeed. (31)
(Noor:31)
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