Looking solely from the point of view of the father of a one year old, and what's different there, I would say: attention. Give him as much attention as you can - probably more than you give your daughter. One year olds need a lot of attention, both to help form a bond with you, and to grow and mature intellectually and emotionally. This will change as he ages, and you can probably lay off some as that happens - but it is vital at 1 to get personal interactions and attention as much as possible. This would be true even if you were living at home with him - that you're not makes it doubly as important.
I absolutely agree that you shouldn't be a Disney Dad, but you can select activities that are more interactive with you and be more conscious to pay attention to him than you might otherwise. Rather than taking in a movie, go to a children's museum where you can play with him; go to a park, and run around with him. Make sure you're still requiring him to behave as he should, and not just picking him up directly to go to the park or whatnot - it should be part of a normal routine, just as if you were there.
When you're at home, read books to him, talk to him. Give him your undivided attention as much as is reasonable. He probably gets less attention than he would during the week if you were there - because Mom has to do all of the housework, perhaps work, and do other things that she would get help with if you were there. During this time - in particular between 1 and 2 - attention and interaction are extremely important to a child.
If you can do other things (like video chat, etc.), I would as well; in addition, create a lot of photos and videos of the two of you interacting. My one year old loves watching pictures of himself and his brother and myself when we do activities - it helps him remember fond times, and is comforting to see familiar faces (including his own).