I think bank app can be assigned to one phone number. But maybe you are just able to login to one bank account with the same credentials on 2 phones (you can try to tell in bank, you have 2 phones ;)).
what city did you have problem? I've never heard that onyone had problem with residence certificate from embassy in Bangkok Bank. But as we know this is Thailand so different branches could have different rules ;)
In Bangkok you can obtain from your embassy - "affidavit of residence". If you have problem with this, go to more expat friendly like pattaya, you should have no problem to get your residence certificate there.