1. Since your mother as well uncle is getting old, it is all the more necessary to apply for the probate of the will at the earliest and complete the process quickly wherein your mother's presence/witness etc is required,
2. After her eventual demise, her legal heirs can step in to her shoes in the said probate case,
3. How are your aprehending that your uncle had already transfered the property to his name? With out valid legal document i.e. grant of probate, registered sale deed, gift deed, settlement deed etc, no body can transfer any property in his name,
4. You can make a search at the egistration office to find out if there is any such deed of conveyance registered in favour of your Uncle. If not, then there is no such conveyance deed in his favour,
5. Even if he has a written will in his favour for the second property, he needs to take probate for it to get it transferred in his name,
6. File a partition suit for the second property wherein all these matters will be cleared.