There will be, as far as I am aware, a CGT liability on the disposal of her share the BTL, but this is the liability of the person disposing of their share.
The link here allows you to calculate the gain:
As to SDLT, as this is payable on purchase again it may be due on your share.
Honestly though, as we are family lawyers and not HMRC agents, the best bet with these questions is to speak to the HMRC helpline - here: https://www.gov.uk/government/organisations/hm-revenue-customs/contact/stamp-duty-land-tax
They will give you a definitive answer on the tax points.
Thank you again for visiting JustAnswer, please do let me know if you have any additional questions in the future. I am also happy to answer any new questions on other topics that you may have, you can request me by putting “for PLCLEGAL” at the start of the new thread. Best wishes, Peter