There's two sets of two sides to this. There's your side vs her side, and there's equitable vs legal solutions.
I'm sure it seems like your sister is being unfair, or somehow greedy, but the reality is that she is 1/2 owner, and you have been getting free benefit at her expense for a long time. I want to say that clearly upfront because I'm sure this is all tangled up in baggage about things like you helping your mother before she died, which is nice, but irrelevant and you have to try to separate the situation from that. If you've got this "I earned the house by being there for mom" complex going on, you must try to get over that. For one thing it's a bone to pick with your late mother for how she drew her will, not a bone with your sister, and secondly it's simply not the reality of the current ownership situation. You say you "can't exactly see that it is right to pay rent on a home I own", except you don't own it, you own half of it, a clear cut fact. You say "especially because my sister doesn't want to live there", that doesn't make sense, imagine a tenant feeling justified in skipping rent payments because the property owner doesn't want to live there...
You have been basically living in this house for free, paying only taxes, which you say don't register with your sister. I wonder if it's really that it "doesn't register", or more that she's shrugging that off as being fine, which is not the reaction you expect. I would guess the taxes+insurance are a few (maybe 5) thousand per year, and comparable rent would be about 15-20 thousand per year or more. You're trying to construe that those two figures are roughly equal and it would be a wash, which it isn't, and your sister is rightly saying "sure paying half the taxes would be a fine deal, if I was getting half of market rate for the house I own half of, and am legitimately entitled to".
Many good answers describe the simple math of paying her (rent - expenses)/2. You could have a real estate agent find comparable rent and do that calculation. This is equitable but not legal. Meaning if she changes her mind in the future about the deal, you have no ground to stand on. This is why (more so than doing battle) it's important to have a lawyer involved and write up legal contracts. You are in a bad situation because nothing was agreed to at the beginning and so neither side will properly perceive fairness. Continuing without contracts leaves it is open to longer, more expensive and nasty legal disagreements in the future. Also, while I say paying the rent would be equitable, it's not entirely -- since you've been living there not paying rent for over 15 years, it could be argued you owe her (rent - expenses)/2 going forward, in addition to back pay (with adjustments for previous rent price trends) for the entire time you've been living in that house essentially 1/2 off of your sisters dime. That could easily add up to more than the cost of buying her out of the house -- such is the dilemma of living in a house someone else owns. However since there was no agreement in the beginning you've probably gotten away with skimming this value from her in a way she has no recompense for - which is legal, but in my view not equitable. Thus the best you can do now, in my opinion, is get out now while you're ahead.
You say selling the house is not an option, but I think you should re-examine and see that it is the only option. Especially if you hope to maintain any relationship with your sister (to preclude nasty family-destroying legal battles in the future). Lets say you find comparable rent and start paying her (rent - (taxes + insurance)/12)/2 every month, and then the heater breaks again and at the end of the year you try to give her a bill for half that and she refuses -- off to court you go against your family. Or she thinks the siding needs to be fixed, but you don't want to deal with it? Or lets say your house floods and you get an insurance claim and there is money left over after the repairs, who keeps it? What if you want to make improvements that your sister would not agree to? Who is responsible for the cost/decisions and how is the benefit divided? What happens when comparable rent goes up significantly and it's time for you to start paying more, who will bring it up and how much resentment accrues before someone does? Every one of these events will create miserable financial/familial tension as long as you remain in the situation.
On the other hand, your sister cannot make you a prisoner to the house for the next 10 years, while expecting this rent as a guarantee until her kid graduates highschool. She refuses to buy you out, that's her prerogative. The remaining options are for you to sell your half, and force her to sell her half as well, (this is the nicest possible bow in which to wrap this up, with the highest chance of still having a family afterward). The other option is you buying out her half, to which you (for unexplained reasons) say "don't even think about it". I can only assume you mean you are unwilling because you think it would be super unfair to you. If so, I disagree, it's the definition of fair. Since you've been living there for free all this time, you could think of it like getting a good deal on backpaying all the rent you ignored for 15-20 years AND getting ownership of the house. A few ticks in your question hint to me that you feel entitled to the house in full, while simultaneously being aware your sister owns half of it. It's unfair of you to imagine that it's unfair to you to be expected to either buy the half you don't own, or compensate the other owner in some way like rent.
Your best hope for your future happiness and family preservation is to recognize emotionally what you already know rationally, that your sister owns half of the house and is entitled to half the benefit of that asset. Either buy her out, paying her what she is legitimately owed -- or get her to agree that both of you choosing to sell the house together is the best path for each of you, and get out of there, close the door on this and move forward with your life. Even if she refuses to sell, getting a court order forcing her to sell her half while disagreeable, at least leaves SOME room to make up and stay sisters after the fact. Whereas staying in a situation where every financial decision in your home has to be approved and/or argued over with your sister, is a recipe for "how much can we hate each other before one of us dies".