I used to be a big pokemon fan back in the day, pokemon might be easier to sell to a parent than the Yugioh thing. At either rate, I would pitch in haveing talked to you.
A card game will always be a card game, it can be fun because it involves tactics and familiar characters. However it is kinda money consumeing in all honesty. Yugioh does involve mythology and magic, which some parents might see as bad. Pokemon generaly involves fantasy and to some extent magic. However, I think if your mom thinks that this is bad for you, then showing that you are in excellent spirtual health is the way to go. Which means do alot of praying, some bible study on your own time, grow closer to God and by all means talk with your parents about it might be a winning combination. While I would not recomend a card game as much as a videogame, I speak from experiense on this, but be mindful over what videogame you potentialy would buy as well.
If she does ask about this place, then tell her that we do consider the bible to be the whole truth and anime to be nothing, but entertaiment which can be either foul or fun. Cartoons genereraly does not seperate themselves too much from anime, although that really depends. Although, at either rate, seperateing reality from fantasy is the key. Knowing which is which and always putting reality first, and being honest on how some media might change oneself if it does so are important factors.
At either rate, talking with you in the chat I think this covers most of it. I hope it answers some of your questions and I hope that it helps.