Teaching the practice of religion as a way of life to kids, is different from what the adults see it in their rational, grown-up perspective. It is somewhat like teaching children "Sun rises in the ____ ?" and he is trained to write "East". Would you teach him, "Sun never rises, nor sets, it appears to do so from the standpoint of.... " ? We would do it, but at the right level and at a time they can catch that more comprehensive view, and onwards from that the kid may even grow up to be an astronomer, but "Sun rises in the east" is relevant at that level. So is the relevance of habits, stories rituals and prayers.
Similarly, to teach kids, you will have to rely on techniques and practices, that would appear "low-level" to an adult. For instance, Hindu parents (well, the ones who care for the kids' practice of it), interweave, Paapa Bheethi (Fear of Sin, not fear of God) into their interactions when they teach about God. Coveting another's property, treating someone unfairly or unjustly, giving undue importance to wealth and social pride, the importance of honour can all be taught from the stories of Ramayana and the Mahabharata. Dunno about this generation, but until the previous one, the story of Karna has been exemplar in understanding charity, friendship, gratitude and discrimination in spite of the complications in his character. What a character, that combines the personality strands, his response to events, his glory and fall, and an individual's place in society !
The daily or weekly chanting of hymns, or the observance of monthly pujas (like Sathyanarayana Vratham on full moon days) is another. This is not restricted to sanskrit hymns such as Vishnu Sahasranama, a popular family chant, but even other language ones like Hanuman Chalisa or the Skanda Sashti Kavacham, that are hugely popular in small town streets. As kids, agree it's just boring rote (okay, nicely followed by some delicious prasadam like Rava Kesari for which we wait with watering tongues), but over a period of time, it has the benefits of memory, concentration and discipline.
Whether a certain religion is instrumental in shaping character in kids, will depend on who shapes it and how consistently, and this is true about any religion. At that point, the practice of the religion is turning to become spiritual, from religious. As a parent, you must be prepared for that transition yourself, because, like they say, children learn from what they see, not from what they hear.
I have myself taught select slokas of the Gita and Bhaja Govindam to teenagers, they are teeming with questions, but if you combine the meaning with a game, a story, a role play or a real-life case study, it would still not answer all of those, but it will sow the seeds. Some slokas from the Gita can be a great starting point for equanimity, self-effort and transcending inferior thoughts about oneself. The sloka 'Artham Anartham' (from Bhaja Govindam), was a serious cause of debate, talking about the intermingling of money and relationships, but as a teenager, when the ritual and mythology has become boring and apparently "unscientific", it becomes a trigger to take them to the next level of intellectual engagement. I would also take them along for a volunteer medical camp or a visit to the government hospital to sensitize them of their role in society. Now, taken in isolation, the hymn has less meaning, but taken together as your walking the talk, it completes it, if not at that time, but at a later time when they grow up and put two-and-two together.
Many modern day values can be traced very well to Hinduism's teachings. Environ care, avoidance of wastage, roots back to the Pancha Bhuthas. Hinduism stipulates five different Yagnas, five different duties of Man, towards parents, towards animals, towards guests and so on. Displaying moral courage for what is right, has its roots in Dharma. Many Hindu prayers have an appeal of universality and progress through co-operation, such as 'Samastha Loka Sukino Bhavanthu' and 'Sahana Vavatu'. We also have extreme ideals like those of Harishchandra. The Hindu stories were the Hollywood of their days, combining drama, dilemma and dharma, you could choose what you want to relish, their character complexity, inner significance, the literary beauty or the lingering feeling of a story that stays with you when you move on.
An endeavour to teach the modern day practice of Hinduism can be a journey for the parents and teachers themselves and this is valid about the true essence of any religion, not just Hinduism. I could easily write a similar one on Christianity or Islam, so it's not about the Hindu tom-tomming.