She has an asset that has appreciated so that, on a sale, she will make a gain and she is required to pay tax on that gain. She needs to stop being disgusted and be glad she has a valuable asset!
Yes, of course, she can avoid CGT. She simply does not sell the property.
Signing the property over to you will trigger a CGT liability anyway and possibly a CAT liability for you and your brother.
She can leave it to you/your brother in her will and that will not trigger a CGT situation but possibly a CAT liability for you and your brother.