This is happening because you are sharing iCloud accounts. When you do this, any synced data such as contacts is merged across devices and the merged list appears on all devices. Also, any action (such as deleting contacts) also happens on all devices sharing the account. To fix this you need to create your own iCloud account, migrate your data to the new account with a different ID, the delete the data you don't want from each other's account. Note: you can continue to share the same Apple ID for purchasing from the iTunes and app stores.
Start by going to Settings>iCloud, scroll to the bottom and taping Delete Account. (This will only delete the account from this phone, not from iCloud. Your mom's phone will not be effected by this.) When prompted about what to do with the iCloud data, be sure to select Keep On My iPhone. Next, set up a new iCloud account using a different Apple ID (if you don't have one, tap Get a Free Apple ID at the bottom). Then turn iCloud data syncing for contacts, etc. back to On, and when prompted about merging with iCloud, choose Merge. This will upload the data to the new account.
Finally, to un-merge the data you will then have to go to icloud.com on your computer and sign into each iCloud account separately and manually delete the data you don't want (such as deleting your mother's contacts from your account, and vice versa).