All of TR's children grew up and where a credit to him. It is interesting to compare his family with the children of FDR. They were a pretty troubled lot. I think FDR's kids got little parental attention where as Teddy was very involved with his children's lives in spite of his busy schedule
TR also chose his second wife very wisely, and she was a good mother to the children. But as a child, how could you not love a man who never forgot childlike loves and enthusiasms? He was also a great horseman (if a bit on the rough-hewn side) and I have to respect that particularly.
Alice was his problem child - I think she really suffered from dead mama/absent father and it shaped her whole life. Nick Longworth was a brave, brave man! But I don't see what else TR could have done but go out West to get himself back together - better an absent father for a short time than a dead or insane one forever.