Unless your mum knows your every move, I do not see why you can’t meet this woman without telling your mum! Surely she doesn’t have to know everything you do? I would suggest to this lady that you’d really like to meet her, but explain that it would have to be done in a quiet and private way in order to avoid your mum finding out. If your half-sister can agree to these terms then I would go ahead and meet her. And please don’t waste any time feeling guilty or disloyal to your mum; you are perfectly entitled to meet members of your own family.