Mortgage Advice please

MrNeedAdvice

I've split from my longterm partner. We have lived in our house for 6 years. Although at the time of purchars my partners financial situation was better than mine so took out the mortgage in their name only. 

We're on good terms at the minute and are still living together for the time being but unsure of the best way to split the house.

My partner has recently set up a new business, so only has around 18 months worth of accounts. Also got a silly CCJ for a £200 parking ticket around 3 years ago which we know has impacted their credit rating. 

My financial situation is now very good and I think I'd have no problem in getting a mortgage. 

So am I right in thinking that we have 3 options?

1- I buy the house at a reduced rate, we have around 50k equity in the house which is worth around 140k. So purchase for around 115k.

2 - we sell the house and split the money from the sale.

3 - they remortgage and do an equity release to give me my share. (this could be tricky with their current financial position)

I should add as I earned a lot more over the last 6 years I've put about 30-35k into renovation so am quite attached to the property. Ideally I'd like to buy it (1st time buyer) but don't want to leave my ex in a position where they can't get back on the property ladder.

Any advice would be very much appreciated. 

Thank you