ANSWER:

It’s not about being younger than the female or not, it’s about being the mahram and the cousins are not mahrams to each other, therefore it’s not permissible for your neice to travel with your son. She must have her own male mahram to travel. 

https://islamqa.info/en/answers/5538/who-are-the-mahrams-in-front-of-whom-a-woman-can-uncover

I am a female planning to go for umrah with my son and want to take my niece along with me. Can my son (18 years old) be a mahram to my 27 years old niece (my sisters daughter)?

Hajj and Umrah, Mahram | November 7, 2018 3:54 am
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Here in India many middle class who do not have much money are going with Package Tours for Umrah and have not done Hajj as to collect money for Hajj will take years.So I told them you cannot do Umrah before Hajj.She replied she has asked a Salafi Imam and he said our Prophet s.a.w did 3 Umrahs before Hajj.Is it correct?
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Bro when we go to umrah from jeddah should we take shower frm home thats enough or must to have shower for womens at mikhaat also.