Hopefully, changing her diet will resolve the wet poo issue — if not, then you need to take your rabbit to a rabbit-experienced exotic vet: https://wabbitwiki.com/wiki/Choosing_a_rabbit_veterinarian#Rabbit_veterinarian_listings … rabbits cannot go to ordinary dog/cat veterinarians.
The poop is likely due to an improper diet. A 12wo should not be getting stick treats nor apples– at this age, your rabbit’s stomach is developing and can only handle certain foods. Tell your mom to wait until your rabbit is 4-6 months old before trying those foods, and if she is, they should be given in small portions over time so your rabbit’s stomach has a chance to adjust to the new food. Small, slow introductions are needed when introducing any new food to a rabbit’s diet.
Right now, your rabbit’s diet should only be rabbit-appropriate hay and good quality pellets. The grain pellets need to be switched out (transition over time) to something healthier. See here for guidance on what pellets are good: https://wabbitwiki.com/wiki/Pellets#What_different_types_of_pellets_are_there.3F … remember you need to transition your rabbit off the old and into the new pellets, so mix the two and gradually add more new and less old over time.
Please see here for proper information on your rabbit’s diet based on age: https://wabbitwiki.com/wiki/Diet#Age
The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.