My sympathies to you Mr G, that's a horribly messy situation.
I was in a slightly similar situation to your sister in that I moved back in to the family home to care for my father, and there were some complications after he died over the delay in me moving out of the home (due to the tenants in my own house being unable to find new accommodation - it was all resolved in the end).
I, too, would have paid for most of the maintenance of the famiy home after I moved back in (for six years), including gardening and decorating costs, but I never once considered that that gave me a right to a larger share of the proceeds of the sale of the house. I don't believe your sister should either - she was living close enough to rent-free in the home (apart from those small mortgage payments), as I was, so contributing to its general upkeep was the very least she, and I, could have done. If she is arguing that she sacrificed a lot financially she needs to ask herself how much she would have paid in rent for the last 18 years if she had to live elsewhere, especially in more recent times with her husband and child. If she had paid for major renovation work on the property, she might have some argument, but not if it was purely for its upkeep.
Most importantly, though, it would appear that it was your mother's wish that the proceeds from the sale of the house be divided equally between you and your sister. Her wishes should be respected.
I would withdraw your €10k offer to your sister, and inform her of that, and use a solicitor to deal with this from now on. I know it's a pain to have to pay for a solicitor, but I think it would be more than worth it for you. Apart from anything, it will show your sister that you are challenging her on this - she, it would seem, thinks she can force you in to meeting her €50k demand by refusing to agree to the sale of the house. I'm struggling to believe she is legally entitled to do this. She might be unhappy with your mother's will - if she is, let her challenge it and bear the cost of doing so.
I would discuss with your solicitor the possibility of demanding compensation from her for the delay in putting the house on the market, the figure increasing for every passing month. That might make her re-think her actions.
Your €10k offer was most generous - too generous, in my humble opinion - the fact that she rejected it suggests she is behaving far from reasonably in this.
Her sense of entitlement, despite her mother's expressed wishes, is a touch ugly.
Best of luck Mr G, again I would strongly suggest you get a solicitor on to this, I have a feeling your sister will soon learn she is not on solid legal ground.