"So I watched Cara Schultz's video on your blogspot about Hecate and household worship. Early on, she said that household worship is passed on. Does this mean it's forced onto your children? I've always promised that I wouldn't force religion on my children and I would be torn between that if I had to honestly but I don't want to displease the Gods."
The video in question can be found here. It's a Google chat session where she spoke to The Order of Hekate about how Hekate was worshipped in ancient times, as well as the basics of Hellenismos. Her talk incorporates Hekate's Deipnon, Noumenia, Agathós Daímōn, household worship, household worship vs. state worship, the future of Hellenismos and interfaith work. It's a long video, but it's very worth it, especially once Cara gets on a roll. Cara, for those unfamiliar with her, is a member of Hellenion, the largest Hellenic polytheist organization in the United States. Her workshops on Hellenismos have been held at some of the largest Pagan gatherings in the United States, including Pagan Spirit Gathering and Sacred Harvest Festival. She is also the Managing editor of the Pagan Newswire Collective and founder of International Pagan Coming Out Day.
As for your question... I don't believe religion should be forced on a child, but there is a difference between forcing religion upon a child and including them in worship. Children emulate; that's how they learn. When they see mommy or daddy raise their hands at the household altar, they will want to do it, too. It's something that their parents do--and obviously like to do--so why shouldn't they? I don't see an issue in allowing your children to playfully participate in household worship. Tell them the stories of ancient Hellas, allow them to grow up with the Gods in their lives if they so desire.
Therein lies the rub, though; this theory only works if you have a child who shows interest in participating in rites and festivals. If your child does not and you still make them... well.. let's say that you and I are off to a rocky start. I firmly believe adopting religion is a choice. It can be made by only by only one person: you. As a parent you have the right--and yes, I think the Hellenic responsibility--to teach your child the ancient ways, but if they say no, then the answer is no. Perhaps they will come to you when they are older, perhaps they won't. That's under their control, and perhaps the Gods, who may call to them.
Back in ancient Hellas this was a non-issue; everyone knew the Gods to be real and the festivals were gran, fun, and came with lots of yummy food and playtime. There were flowers and pretty clothes and days off. Festivals were brilliant times for kids and of course they participated! Our modern rites are often not that grand, and a lot less exciting for kids. Some children will be drawn to them, others won't.
We, as (future) parents, pass on what we know. Especially Hellenismos--which is a household religion--serves from initiating the new generation into it, but there are limits to what I think you are ethically allowed to push onto your children. I would say the general guideline is: 'are they going to turn out assholes or end up dead if I don't? Yes? Then tough luck, kid, you are learning this'. Religion is not life or death, and being non-religious or finding faith somewhere else does not make you an asshole. So no, I don't condone forcing religion onto your child if they don't want it, and in Cara's defence, I highly doubt she does either.