OK, wow thats a hard one, I'm 24/7 IC and my dad still has no clue.....
guess it depends on how understanding your dad is. my mom understands my diapering and is helpful with it, but I'd never tell my dad because he's not understanding of anything. So if you two don't have the greatest relationship, your in a rock and a hard place. But as painful as it may be, I'd be honest, it's easier than hiding it for the rest of your life. So here goes:
If my dad found my diapers, here's what I'd do: I'd be honest. I'd say I wear diapers, I like my diapers and they make me feel better-happy-etc. I'm not out doing drugs or drinking, I'm not sleeping around or anything like that, I'm not hurting anyone. I simply like wearing diapers, if thats the worst thing I ever do, I'll be proud of myself. and yes, it's seems like the a weird out of place thing todo, but it's part of me, and it doesn't change how I love you and as my dad I hope you see me in the same way. Thats what I'd say.
I know what your going through is hard time, I had a friend find out and it was painful at first, but it didn't change how they felt about me as a friend, and they continue to accept me and my being IC/DL. Hope this helps, I'm sure everyone else well chime in with good advice, thats one thing you have going for you, being on adisc.