About as close as distant relatives are in a big rich family. There was a small (I can't really remember the particulars right now but it seemed small to me I remember. Certainly it was no Hatfield/McCoy drama) dispute going on most of that time they were both still alive so those factions weren't really talking.

Teddy seemed to really love the hell out of Eleanor. I don't remember if he was tickled or just mildly accepting of their marriage but that seemed to be a notable break in the silence when FDR and Eleanor were married.

But to me that doesn't matter as much as how clearly FDR admired his cousin. I think that inspired him to go the route he did. I mean taking the same political steps is probably a pretty clear indication. Life got in the way a little... Yes I realize polio isn't anything easy but he sure tried to make it look like it.

Anyway, I haven't seen anything address the intersection of Teddy and FDR like the PBS series "The Roosevelts" which might still be available for streaming. Even though Ken's work isn't taken seriously around here, the section of history you're asking about, I think, was covered quite well in that documentary. http://www.pbs.org/kenburns/the-roosevelts/

One thing they did absolutely share was an in interest in the sea and a deep even love of the the Navy and the seagoing service.

Early on TR gifted to Franklin a copy of Mahan's seminal work "The Influence of Seapower Upon History" and Franklin was very complimentary of TR's history of the USN during the war of 1812. And they had an ongoing dialogue about the Navy's role in the growth and assurance of the United States as a world power, and in particular her ability to fight a multi ocean war.