Wishing to Travel on Shabbat for a Positive Purpose

Hi, I am a former yeshiva student, currently not religious at all. I have a cousin who is hospitalized in Jerusalem due to a respiratory infection. He and his parents are completely Haredi. I want to visit him during the holiday and Shabbat. I drive and walk on Shabbat anyway, and I want to do something positive along the way. I need to ask his parents for permission to meet his secular cousin, but they are busy and won't have time to ask a rabbi, which will make them answer that it's better I don't visit. So I'm asking on their behalf if it's okay for me to come visit, considering I don't discuss religious topics with Haredim.

Hello and happy holidays!

I did not see the question before Shabbat, so I could not answer in time.  Nevertheless, I will address the question, which is relevant to you in other events, and also to other readers:

Your desire to help your cousin is positive and shows your good heart. However, in practice, you are not allowed to travel to visit him.

Let's detail the rules concerning this:

There is no permission for someone who does not observe Shabbat to perform work on Shabbat for someone who does observe it. 

Work done in violation of Shabbat is forbidden for a Jew to benefit from on Shabbat, and sometimes it is forbidden for a Jew to benefit from it forever.

Even when a person did the work for themselves, there is no permission to use what they did. 

For example, if a person who does not observe Shabbat calls an elevator for themselves to a floor I need, I am not allowed to join their ride or transport an object in the elevator that I want to bring to that floor. 

Shulchan Aruch, Orach Chaim, Siman 318, סעיף 1