1. I assume that your mother has never applied for one. I don't see the point why she will be denied (only people who applied so often may face such result).
2. Yes - Re-entry permit is not a safeguard or insurance for not to lose your residency. If CBP determines that you do not have the intention to remain as a Permanent Resident, CBP can still confiscate the card and refer the case to Executive Office of Immigration Review for determination.