(((((((Kalni))))))) I know this is such a painful time for you, I'm so sorry for your loss. Your dad sounds like a wonderful person. I has a few thoughts that may or may not be helpful...
(1) If you are like me, you'd like H to sit next to you, stroke your head, just be with you. But, H is obviously an acts of service guy. He is *doing* everything he can to love you and support you. Feel that the way you'd like to feel it right now. The next time he takes care of something, close your eyes, feel his body next to yours on the couch, his arm around you hugging you tight saying "oh baby I love you so much everything will be all right." Because that is what he is doing. Feel it the way he means it -- translate inside. Maybe it sounds hokey, but it really works. Also, it might not hurt to ask explicitly for what you want. "I'd really like for you to hold me, pat my back, murmur comforting words, and then tell me to get butt dressed and go for a walk with you." Texting is fine and maybe easier for such things.
(2) "My love, my eyes." If that isn't enough to make anyone cry in a good way, I don't know what is. Perhaps if you stop telling yourself how you ought to be doing and give yourself permission to mourn and love your wonderful daddy, you can do it in a way that moves you forward with him in your heart. Can you take some space each day to do something that would be loving for you both? "See" something for him, do something you would both enjoy, and make sure you leave time to laugh or cry about it? Then, put it away until tomorrow with love. Not forever, not to be done with it, just put it away until tomorrow when you can do a little more mourning and keep a little more of the love. Maybe that would help. Right now I get the sense that you are being pressed down with the weight of feeling like you have to be "over it" all at once. Poof. Well, it isn't going to happen. So, let go of that weight, dump it in the bin. A little each day. Respect and love yourself and your father by giving yourself permission to try it that way.
(3) Your anniversary. Well, doing (1) above might help with your apathy there. You might be a wee eensy bit passive aggressive there because you aren't getting what you want from H. But, it is also NORMAL. Still, it is worth consciously affirming that it is OK to look forward to things and to enjoy them. It does not mean you love your father less if you do so. It is OK. Also, (perhaps weirdly) it might help to forget about yourself in an odd way for a minute. Suppose you have a friend who has an anniversary coming up who doesn't know what to do. Help her out -- what would be a fun, loving, meaningful activity? Finally, another way to think of it is not about it as something important to you but as a loving gift for H. If I'm right that H is an acts of service guy, it would probably mean a WHOLE LOT to him if you get off your butt and make something happen for your anniversary. That you did it at all and especially now will not go unnoticed. Imagine yourself getting the plans together in a big shiny gold box with bows and hearts for H. (Or, maybe that should be you in the box, lol.)
Hang in there. It is hard now. It will get better. Howl at the moon if it helps. A support group might be another way to find and protect space to mourn and space to live and love. I had a C once who told me that NO ONE will ever be EVERYTHING we need. It is best to recognize that and own that WE ourselves are the ones responsible for making sure we have everything we need, and doing so means getting those things from different places sometimes.
Now, unless it is raining, bundle up, go outside and walk at least one mile. Now. Do it. Do it. Do it.