The teenagers are his and therefore his responsibility. The house is also his and therefore also theirs.
Presumably he asked you to live with him/them, not to take on joint ownership of the house. Therefore the house insurance isn't your responsibility, along with anything that goes wrong with the house, including the appliances - as these are his responsibility.
His kids are there quite a bit, from the sounds of it. I would not expect a partner of mine to pay 50/50 towards the running of a house that was also my children's part-time home.
It does look like you're simply sharing his expenses with no benefit to you whatsoever.
I'm a single mother, with children so obviously my children are here the majority of the time when not at their dads.
Let's say my kids are at their dads the same amount as your partner's kids are with him - 1/3. This would mean they are with me 2/3 of the time. I would not expect my future partner who was not their parent to pay 50/50 of the running of our home if he was living with us, because the children are not his and not his responsibility, nor does he have any financial investment in our house.
Whether it's their main home or their part time home, it's still the children's home. Therefore, this part needs to be covered by their parents whose house it is, not you.
It's only pedantic if the parent responsible for them doesn't see this obvious flaw when wanting to charge you 50% of the running of their home.
How about this:
Let's say he owns a huge castle with 85 bedrooms - there is no mortgage on it as it's been in his family for generations. It would cost a fortune to run, certainly much more than any normal house. But it's his investment and has a lot to gain from it eventually.
So there he is bumbling around in his castle with his two teenagers who like to spend 1/3 of their time there and the rest at their mum's. How he affords to run his castle is his business, but he manages.
He eventually meets a lovely lady who lives in a small house. She only has to pay the smallest bills in her house as her consumption is minimal due to only her living there.
Castle man eventually declares he has fallen in love with her and asks her to move in with him. He says she needs to pay half of everything if she agrees to move in.
Q1. Should she be responsible for 50% of the running of her boyfriends castle?
His property is obviously much larger than her house she owns. Living in his castle has no benefit to her whatsoever, and moving in would not automatically mean she owns part of it, which means has no investment in it.
He is adamant she should pay half of the cost of the castle even if it means she pays out more than what it costs her to live in her current house. She also has to pay half of the council tax, property insurance and utilities.
As she thinks about it, she realises that living in a property of that size is of no benefit to her and she has no interest in it, so she begins to wonder why castle man wants her to stump up 50% of the costs of running his castle?
Is he taking advantage of her, or is he being fair?
I personally think she should only pay a contribution to the amenities that have increased due to her taking up residence there, so heating, gas, water and food.
She already has a firm idea what she costs in relation to these, as running her own home will reflect thrse costs beautifully. She should certainly not be paying any more than that.