Re: Quick claim deed
A deed in proper form, whether a grant deed or a quitclaim, transfers the grantor's title to the grantee(s) upon its delivery. When recorded, the deed is "notice to the world" of the things set forth therein, but even an unrecorded deed is valid and binding as to the parties and anyone with actual or constructive notice of it.
Once the deed was executed and delivered (and absent invalidating circumstances such as fraud, duress and undue influence), your mother irrevocably gave up the interest granted by the deed. If she still retained a life tenancy, she has whatever rights were retained, but a life tenancy cannot be inherited if the "measuring life" is her own.
To give you an idea of the permanent and irrevocable nature of a deed, the grantee can tear it up the day after it is delivered, but even if both parties intend to cancel the deed by destroying it, this act is insufficient to un-do the transfer. In order to reverse the transfer of the property, it would be necessary for the grantee to grant the property back to the original grantor by a new deed.
Now, a few words of caution. First, it's usually a bad deal tax-wise to transfer appreciated property before death - generally you avoid capital gains taxes by using a trust or will rather than a deed and life tenancy.
Second, co-ownership by three brothers is likely to lead to future disputes such as whether, when and how to sell or refinance; who pays the property taxes and insurance; who gets to live there and/or who may act as manager if the property is leased. I advise the brothers to negotiate and sign a contract covering these issues and perhaps including buy-out or right of first refusal provisions.
Finally, within-family transfers are sometimes done in an ill-advised attempt to place the property out of the reach of creditors such as MediCal or prospective judgment liens. Such transfers are a fraud on the creditor and can be un-done by a court proceeding. These warnings are added not because I detect any such problem here, but because LawGuru answers are read by others who are looking for advice and may be considering such a maneuver.