Hi, there thanks for the additional information! Ok there are a number of questions here, so I'll try my best:
Q1. Is the proposed verbal agreement reasonable?
A1. I think you are taking a risk by not writing down the agreement, and I think you are being quite reasonable. I would suggest that if you agree in principle, to get it in writing as soon as possible and give her a time limit - such as: she has 6 months / 12 months to pay you the money (by refinance or otherwise), or she releases all claim over it. Also, make it a condition that she pays the mortgage which she is living there - especially since she isn't working right now. After you get the informal agreement signed, get the Court to issue a Consent Order in the same terms - this will make it legally binding on both parties in which case, since you have both agreed there is no further issue of reasonableness. Definitely go the route of a Consent Order. While she is in a mood for negotiation, pin her down to an agreement. It will save you money and time in the future.
Q2. Can the bank take the property?
A2. Yes if the mortgage payments aren't paid, and subject to the loan contract. That's why either you or she has to keep up the mortgage.
Q3. Does your ex have any claim over the property at all?
A3. Yes. So long as you were a de facto couple, she will be entitled to some share of the overall property - but as I said before you can agree to the split, and this will provide you certainty.
Hope this answers your question - once again, quite happy to clarify if I've missed anything. Regards, Jared.