Hello again & thanks for the extra info. Sorry for the delay in getting back to you.
To start with, you & your wife can agree whatever you want with regard to the ownership of the property currently in joint names, and how much if anything you pay her in return for her share of the equity -
if you want a legally-binding agreement ie one that neither of you can overturn at a later date, then you will need a court order. The power of the court to make orders in relation to matrimonial property and finance only comes into play once a divorce petition has been filed at court - so the first stage is to issue divorce proceedings.
Regardless who files the petition, either one of you can apply to court to ask the court to decide how the matrimonal assets should be divided if you can't reach agreement.
The matrimonial assets are everything in your name, everything in her name, and everything you own jointly. So it won't make any difference to her entitlement to make a claim if by the date that a divorce petition has been filed at court, the house is in your sole name.
The fact that she has committed adultery will not affect the outcome one way or the other.
The fact that she has a new partner also won't affect her share of the assets - but if she and he start living together, then that will affect the outcome because she will have an increased mortgage capacity, and so will not need such a large share of the assets to rehouse herself.
Both parties are under a duty to provide full details of all their financial circumstances. If it's a contested case, each party has to complete a 28 page financial statement. If agreement has been reached, and a solicitor has prepared a draft order by consent (called a "consent order") for the court to approve, then only a summary of both parties' assets is required.
The court starts from the position that the assets should be split 50:50, and then considers reasons why that might not be appropriate eg if one party has a significantly lower income than the other or is caring for dependent children. In your case, your incomes are the same - but you might be able to argue that you need a larger share of the assets because you are going to provide a home for your oldest child for the foreseeable future.This would be unusual as he/she is not a child - but not impossible. On that basis, you might be able to argue for 60% rather than 50% - but it's unlikely to be more. But whatever your share is, you will be expected by the court (if you want the court to approve a draft consent order - which is the only way to get a legally-binding consent order) to buy out your wife's share, if the property is to go into your sole name. If her share is 40%, that =.4 x £70,000 = £28,000. However, that would mean that you would need to be able to cover both the existing mortgage and debts of £100,000 plus an additional £28,000 - but no building society will give you a mortgage of £128,000 - and I would also doubt that any building society would even agree to transfer the mortage of £100,000 (if you paid her nothing) into your sole name. On your income of £18,000, your mortgage capacity is £18,000 x 3 = £54,000, or possibly x 4 = £72,000.
The aim of a court order is to achieve a "clean break" if at all possible ie to end all financial ties between the divorcing couple, so if the house stays in joint names, that has not been achieved. Another option would be to sell the house, and to divide the sale proceeds in agreed shares eg 60: 40 in your favour - thus would give you 60% x £70,000 =£32,000. That would be your deposit, plus a mortgage based on your sole income of £54,000 = £86,000 - but would you be able to rehouse yourself and your eldest for £86,000?
Where there are young children, a court order can state that the house be sold, but not until the youngest child finishes their education, at which point the house is sold, and the proceeds shared as agreed - but in your case, there is no clear end date in the future when your eldest will be able to live independently, so I think a susoended order for sale is unlikely.
If your wife's name stays on the mortgage, then this will mean that she will nto be able to get another mortgage, wich means that she would be unlikely to agree to a suspended order for sale.
I'm afraid that there is no clear-cut solution to your situation - things are always more difficult to resolve when there is less to divide up.
I strongly advise you to get some face-to-face legal advice. Here's where to find a specialist family law solicitor near to you:
It's far better to negotiate a settlement than go to court (which is stressful, time-consuming and expensive). You can negotiate either between the two of you, or via solicitors' correspodnence or via mediation. Here's where to find a family mediation service near you:
I hope this helps and I wish you the best of luck.
Thanks and best wishes...