I see, thanks for that.
A couple of more questions for you, please bear with me.
I'm not surprised that AISH is making her take you to court. Even if she acknowledges that she's put nothing into the home, she's on title and thus her entitlement to social services benefits is impacted by the fact that she "owns property". This wasn't her idea I'm sure, so I hope that you two aren't fighting about it. They made her.
Are there any other significant matrimonial assets or debts? Since the mortgage was essentially a "consolidation loan", should I assume that you're paying the mortgage solely?
Your father gave you the home as a present? I assumed that you got it under his will, that's far more common. When he transferred it, it went straight into your joint names? Unfortunately this will mean that it's a gift to the two of you, unless there's something in writing to say that it was a gift to you specifically and that it's to be excluded from any property division in the event of your separation (even then it's not a slam dunk that the equity would be solely yours).
You say that you made a stupid mistake to take out a mortgage to consolidate other debts. Don't be hard on yourself, as that was likely the right decision to make at the time. Can you tell me what debts the mortage proceeds covered?