Or you could keep it simple and say: I made a card for my Dad.

Both are fine. If we are talking fine nuances, the first emphasizes the importance of the fact that I made the card myself (rather than buying it), and the second that I made the card without assistance.

I think it is better in this order but I also think writing by myself isn't necessary as you have already said "I made" which suggest's you did it by yourself anyway. I made a card for my dad, by myself.

Both of those are correct english. The phrase ¨by myself¨ means that you did it alone, without anyones help. Saying ¨I made the card myself¨ simply means that you were the one who made it, others could have helped.