When Shinjuro first brought him home he was so scared to leave his side. He ended up staying home for close to two weeks because Iguro would have a panic attack every time he tried to leave.
Shinjuro was given two choices when it came to Obanai. Let the core raise him, or Shinjuro could raise him. Shinjuro chose to take him in. He was essentially raised by the core and being trained half to death wasnt going to be an option for Obanai.
Shinjuro felt responsible for him since he saved him. The child had nothing, and he already gotten very close to Kyojuro and Senjuro by time Shinjuro was told to make his decision. He refused to take that away from him.
While he was drinking a lot still he was taking care of the three kids. He very much regrets all the drinking. He lost both Kyojuro and Iguro before he was sober enough to at least apologize and not let their last actual conversation be a fight. He didnt want that, and he is very aware its his fault.
Iguro and Kanroji are burried together next to Kyojuro and Ruka. The spot to the left of Ruka is reserved for Shinjuro. Iguro and Kanroji are the first people to ever be burried on the Rengoku family plot to not have their blood. Shinjuro knows very well its a family plot and burying non family is frowned upon. But burying his son and his should have been wife there didnt feel like burying anything but family. It all hurt the same, so it surely wasn't too different.