Is not informing the bride's family of my chronic illness considered a betrayal to them?

If you inform the girl about your illness and she accepts it, there is no need to inform her family unless the illness is one of the defects that necessitate the option (of annulment). In that case, her guardian must be informed, because the right is shared between her and her guardian. He has the right to prevent her marriage due to harm and disgrace, unless they both agree and accept it, in which case it is permissible.