These wonderful ladies have given such sage advice already, that I agree with whole-heartedly. I understand what you are saying, and I think it is equally heart-breaking when some adult family members I love so much are not taking the Lord to heart either.

If I let myself dwell on it, I could break into tears at any moment. I do believe that the Lord saves, and as much as I want to - or you want to - we just cannot. But, the one thing that has made a huge impact on my dc as well as others I love deeply is first, me working on my own faith which could always improve, and second me trying to share my faith as much as possible in just the day to day.
For example, I try to listen to mainly all Christian radio/music, and sing along with heart at home. When I'm stressed or in a bad mood and need an attitude change, I tell the kids I'm upset (they usually know already

) and I need to fix my attitude. So, I turn on a favorite Christian CD I have and make myself sing. Of course, when in that mood, it is difficult to be cheerful, but I have found that not very far into the song I am usually able to change my attitude and after awhile, even laugh at myself with the kids when I realize how ridiculous it was I was that upset about something that is usually quite trivial in comparison with the hope I have in the Lord. I try to do my Bible quiet time each day, though I miss days admittedly, but most days I am doing it, and sometimes my kids just come in the room and find me doing it or praying. They know not to interrupt me, as I let them know that this is my time with God, and it's very important to me. I've said this so many times (you know how good dc are at interrupting once we start a Bible quiet time

), that I've heard my ds peek in my bedroom when I'm praying, and quickly heard the door shut as he whispers to the other 2 little ones, "Hey - quiet, mom's talking to God and doing her quiet time." Little things such as that make a lasting impression sometimes.
Lately, I started a prayer journal with the dc, letting them know the reason for it was I was forgetting to pray for some people/situations I wanted to, and also that I realized sometimes we are forgetting the many, many prayers God has answered as we just move on to our next requests.

I pointed out that their prayers were seeming to be kind of lifeless too. We take turns being the "lead horse" for praying. The prayer journal has helped them with their prayers.
Sharing my heart with them, and what God is doing for me or how I get through tough times by leaning on Him are both important to share with my dc. I try to let them in on some of my struggles (the ones appropriate for their maturity level

). Like, I really miss their dad sometimes when he's gone, and how I couldn't do it if I didn't know the Lord is always with me, that I'm never alone, and that He is watching over me loving me so much. Little things, like writing a Bible verse in their b-day cards and telling why that verse reminds me of them, or putting Scripture verse art/decorations on the wall, or making sure to give something Christian for Easter, Christmas, etc. all are simple things to do that can make an impact over time. I try to do this with are non-believing family I love as well, in a non-preachy way. Where we spend our money is a big indicator of what's important to us for our dc as well, so I firmly believe we can never have too many Bibles, story Bibles, Christian music CD's/videos, etc. in the house.
We started reading through the Bible at night, one section at a time. We read through Matthew, and now are almost through Mark. We just informally discuss it as we go. Another thing - when things are going wrong, just asking them to pray with us - which I need to remember to do right away more often

. That shows we really believe in the power of prayer because we depend on it. Trying to make Sundays as happy of a day as possible is important too. I used to feel so rushed, snapped at the kids, did errands before/after church sometimes - all of that was not good. Now, we try very hard to make Sundays enjoyable and as stress-free as possible. We don't get groceries on Sunday anymore, we have baths the night before, set out our clothes, all the kids have special Bibles/Bible covers for church, go out to eat every other Sunday as a family (which we NEVER do otherwise), etc. Also, during church, each of the dc must take notes, and I do too. On the way home, we discuss it all together in a "what do you remember/find interesting" kind of way rather than in a "quizzing" kind of way.
Anyway, even though I know we don't have the power to save, I want to be doing something to share the Lord with those I love. These are a few of the things I've really enjoyed doing, and though I never get them done all at once, they are easy enough to get done often. I hope something here can help, but you know praying for our dc (and whomever else we dearly love) to be saved by God's grace daily, for the Lord to enter their hearts and be real to them, is a prayer to try to pray daily for each person by name. This is a constant in our prayer journal.
In Christ,
Julie