The first rule in data storage is redundancy, so the best solution is to burn a copy on DVDs and keep another copy on an external HDD. in this way it’s safer. Also the way CDs or DVDs are stored is important, because for example leaving discs under the direct sunlight certainly will make them unreadable very quick.
Another useful trick is burning data on discs adding in it also some sort of parity data, useful to recover the disc contents if some sectors become unreadable. For this there are various tools, like DVDisaster.
If you already have a good burner, maybe the best thing is buying an external HDD (I suggest a good brand, to ensure quality, like Western Digital or Hitachi). In this way your mom will have a copy on a HDD, and you can use the drive to burn the pictures on DVDs or CDs.