The question posed needs more details to adequately answer the question thoroughly. If one wishes to seek an injunction, one must first have a lawsuit on file. There are specific legal elements that need to be meet and you must be prepared to post a bond should you prevail on the injunction.
You do not automatically become custodian of your children's UTMA accounts just because the custodian died. Was there any paperwork submitted naming you as successor custodian? If you are just asking Chase to appoint you as successor custodian just because you are the parent of the minor for whom the account was set up without any paper work naming you as custodian then Chase is correct.
You need to see a lawyer who can review the documentation and provide you with advice particular to your situation. Your real question (how to get a successor named/ appointed) cannot be answered without reviewing the relevant paperwork.
DISCLAIMER: THE INFORMATION PRESENTED HERE IS GENERAL IN NATURE. IT IS NOT INTENDED, NOR SHOULD IT BE CONSTRUED, AS LEGAL ADVICE. THIS RESPONSE DOES NOT CREATE AN ATTORNEY-CLIENT RELATIONSHIP BETWEEN US. YOU SHOULD CONSULT WITH A QUALIFIED ATTORNEY FOR SPECIFIC LEGAL ADVICE ABOUT YOUR PARTICULAR SITUATION.