OP, you need to meet your sister half way and talk about the price, the timescale, who negotiates any offers if they are below asking price etc etc.
When you offered your sister a 20% share you could have said 'and I understand that may not be of interest to you, so if not, let me know and we can discuss how to get the sale underway'.
But you are sitting still, not being pro-active, and then being unhappy at whatever your sister does.
I know it's hard, and its bad timing, but take your half of the control, engage with the process, get your money, and you might feel less hard done by because you have actually taken part.
And don't do any silly deals like becoming half owners with the tenants.
Sell the house (if you can do neither LTB or BTL) and think very carefully about using the money sensibly to invest in your life - paying off your current mortgage, or whatever. You will be needing to manage without the rental income, so think about your budget, and whether you can use the money to lower your monthly mortgage payments.
Also - remember you will have capital gains tax to apy.
And have a look at the regs about the costs of buying if you own more than one property - I believe you can claim the extra back if one is on the market and is sold within a year, or something.
Be smart, be active, make this work for you.