Yes washing clothes in laundry detergent does help to kill the MRSA.
Wash clothes and bedding often using hot water when possible and use a good laundry detergent which helps kill the MRSA.
Drying the clothes and laundry including bed sheets also helps to kill the MRSA and disinfect all surfaces that the person may come into contact with using a disinfecting spray and even Clorox Wipes.
Also having MRSA does weaken your immune system.
The MRSA compromises the Lymphatic system which is crucial to a properly working immune system and when that Lymphatic system is compromised your immune system is weakened.
MRSA is highly contagious to family members or anyone else that is around the person who has MRSA.
If someone in your house has MRSA then it's highly likely that the other family members or at least one family member in the same household will get MRSA as well.
MRSA is a highly contagious disease that can easily spread through skin contact.
If someone has MRSA and you need to touch the person you should wear gloves when touching the infected person and always wash your hands with hot water and antibacterial soap often.
Use disinfectant on things that the person with MRSA touched and wash the bedding and their clothes often as well.