Just be honest with your parents. They may be angry for having to pay for another retainer but it's less expensive than going back into braces because your teeth are shifting. You won't be fooling the orthodontist so I would tell your parents before the appointment and get the anger out of the...
What you are referring to is "fixed" retainers. They are not necessarily permanent as they can break, come loose, etc. There are a lot of factors to consider when choosing to get fixed retainers, including how the initial alignment of the teeth was, how is oral hygiene, condition of gums and...
It is difficult to tell from your photos exactly what is going on. A visit to your general dentist will put your mind at ease. There are many causes for the point going away. Your dentist should be able to he you.