Your church should really just be using a lot more English, since it seems that a decent sized portion of the population is having a disservice perpetuated. Maybe it will happen in another 20 years when this generation is completely lost from the Church, too, and the churches are empty...but then it may be too late.
I love seeing children sleeping at the services. Children should be brought to as many services as possible--and if you really want to help her with experiencing church and being a religious person, say daily prayers with her. They can be the 3 minute-in-and-out that a 9 year old with today's modern attention span may be able to handle--even just the Trisagion prayers and maybe a prayer for the day. Church shouldn't be just something you do on Sundays, not just something you sit through, but part of your everyday life. Bring her to as many services as possible, no matter how much she whines--nearly all kids whine about going to church. Don't let it be a passive experience, where you just observe what is happening, but learn about the services, and even if the yiayias glare at you, whisper an explanation for each part to her, explain the things in the church, the icons, the imagery, the theology. If she starts to learn the services and what is happening in them, she might find it easier to follow (even in greek) and therefore start to care more.
Find games to play with the Liturgy. I, without ever looking it up in advance (I didnt know how, for one) would always try to guess who the Gospel was going to be according to on any given Sunday. (Luke! oooh, I was right!)
Make this all part of her life and part of who she is and, most importantly, who she is in GOD, because Church is not a spectator sport, and if she doesn't connect personally with God in worship and prayer, she'll never understand that.