Thanks for your question - I am Sam and I am one of the UK tax experts here on Just Answer.
I am afraid you would be subject to the additional 3% stamp duty surcharge as your wife already has part ownership of another property with no plans to dispose of this to make this new purchase.
The only way around this is to sell or gift her share of the original property prior to this purchase
Let me know if I can assist further
Thanks for your further question - which really should be listed as a new question with a new amount offered, but as this seems to be your first time on Just Answer. I will answer on this occasion.
On a purchase of £340,000 total stamp duty of £17,200
But if your wife sells or disposes of her share of the original property within 3 years then a refund of £10.200 would be due
Let me know if I can assist further but if you have all your need, then it would be appreciated if you would rate me for the level of service I have provided (or click accept)