Here is what I think: You need to sit down with the dentist that is advising you to remove the veneers and ask him/her
1) Why does he think the current veneers are making your gums bleed and be in pain? I think it is important for you to understand why this is currently happening to you. And just how is getting new ones going to fix the problem?
2) Is he going to use different type of veneers that he think will be better?
Seems to me you have not asked these questions to the dentist that wants to do the work. It is important for you to fully understand why the dentist is suggesting what he is and how it will make things better for you. Keep questioning him/her until you have a full understanding.
3) Also ask if they can suggest a different type of treatment then the veneers.
4) Have you spoke to the dentist that put the current veneers on? If they did not put them on correctly or they need to be fixed should they not do that for free? If the error is on them I would think so.
Anyway good luck