In my experience there is a big variety in the family-friendliness of CofE churches of any kind; Anglo-Catholic and moderate are just as likely to be welcoming as evangelicals - or not! There is also a big difference as to what 'family-friendly' means - some think that this means providing a creche/Sunday club/ Sunday school during services, whilst others see separating children from their parents as not family-friendly and instead expect children to stay for the whole service. If the latter appeals to you then look out for All-Age worship. IME it doesn't work that well for under-5s but that is probably because the church where I used to worship refused to provide toys or a soft safe area for them to play in.
I used to be a very committed Anglican but have now left the church, because, like you, I'd become very disillusioned. Whether you find the same problems in the CofE as in the RC church woudl depend on why you are losing faith in it to start with - I know many former Rcs find a home within Anglo-Catholicism and most Anglicans I know love the church despite its failings - I'm just really intolerant!
I agree with you totally that having Jesus in your life is more important than what church you go to. I also believe that the church should reflect Christ-like values and I no longer found that within the CofE, particularly at my local church. I now take our dds to a Baptist church at least once a month - theologically we are miles apart but we are made to feel a valued part of the fellowship, it is very child-friendly and there is no pressure on us to conform to any of their beliefs.
In terms of raising children as Christian, we started from day one, and believe that what happens at home is more important than what happens at church. From when we've brought them home our dds have been sung Christian songs, and prayed with. We also have a lot of spiritual imagery around the home, including in their bedrooms. There are crosses in most rooms in the house, and also madonnas and angels, but we also have things like crystals and natural things; in the playroom there are photos of a mountain stream, an ancient forest, and some cloisters at a ruined abbey on the walls. With dd1, we taught her to say 'god bless' at bedtime when she was two; and two and a half we added a 'thank you' prayer each night, where she chooses things from the day to thank God for, and now at four we also use a simple version of The Lord's Prayer. Dd2 (just two) is a bit different in that she fights going to bed and won't be read to at any time of day, so at the moment I say her prayers for her at bedtime. Both girls have the Lion 'My Very First Bible' and 'My Very First Prayer Book' which are great for this age - for older children Lion also do great Bibles etc so their website is worth a look. Also check out familypublications.co.uk which are Catholic booksellers.
I think it helps to think about how God speaks to you, and how you felt him as a child. For me, nature is very important, so I try to share this with our dds, and say something like, 'Isn't that sunset lovely? It reminds me how much God loves us'. I also love music so try to play a lot, not specifically Christian, just stuff that moves me - the other day dd1 and I were dancing to 'Somewhere Only We Know' by Keane and it was one of those spine-tingling moments where you really know how much you are loved. When the girls get older I've no doubt they'll find their own ways.
Children learn by watching us too, so we try to include them in trying to live in a just and compassionate way as Jesus teaches us to do, and set an example ourselves. This might mean getting the dds to sort out their toys for charity, buying Fairtrade, recycling, sponsoring a child in Africa, inviting a lonely neighbour in or joining a campaigning organisation like Cafod, CND, Greenpeace or the Refugee Council. We also try to have daily things like lighting candles and marking special family days like when dd1 goes back to pre-school after the holidays, or when dd2 passes another milestone. But I have to say that right now I'm rubbish at all of this - with two aged four and two and ds due next month I'm shattered! I'm glad that we have brought them up to believe though; tragically one of dd1's best friends died recently and she worked out for herself exactly where he is - safe in God's hands - and she ven drew a picture of them and gave it to his mummy. It's still been very hard but at least she's had a way of coming to terms with her grief.
hth!