I asked for the account number or name of the entity on that account,
and they refused to give me that information.
If the transfer was made directly from the card to the destination account, then the destination account should be on the transaction record for the card. Asking the bank for this is suspicious. The account owner would have that information already, and they're not going to provide it to someone who isn't the account holder. Following the money isn't the way to go here. Instead, close the card and make sure both the card issuer and the credit bureaus flag this as fraud.
If this was done by getting a true cash advance (cash from an ATM, for instance) and then depositing that cash elsewhere, then the bank has no way of knowing where the money went. Once it turned into cash, there's no reasonable way to trace it after the fact.
I asked the bank for the ATM security footage and they wouldn't give it to me.
Potential privacy issues aside, providing this footage for someone is not as easy as they make it look on TV. Whoever you talked to almost certainly doesn't have access to this footage, there's either a security department that manages it or it's handled by an external security company. Finding the footage from the same point in time as a specific withdrawal involves time-consuming research work by multiple people on both the bank and security side. If the bank volunteered to give out that footage to anyone who requested it, they'd waste a massive amount of time and money. The bank won't even give the police easy access to that footage. Essentially, you need a warrant, court order, or similar legal demand for the footage. That will certify that there is a legitimate need for the footage and that the footage has a good enough chance at being useful to be worth the hassle and expense. It also lets the bank know that you're not some criminal asking for footage so that you can analyze camera picture quality and coverage angles in order to plan your heist. ATMs are common targets for theft so banks are extremely picky about anything that might even theoretically compromise their security.
When I asked who cashed the check, they wouldn't tell me.
You asked the wrong question. They can't tell you who cashed the check because strictly speaking, they may not know (especially if it was cashed somewhere else). You should ask for a copy of the cancelled check. After a check is cashed or deposited, your bank should make available to you either a copy or a digital image of the front and back of the check. You will be able to see the handwriting of whoever wrote the check, your forged signature, the signature of the person who cashed/deposited it, plus identification markings made by the bank where the check was deposited (institution name and location, timestamp, etc). Some banks make these available via online banking, and at some banks you have to ask for them. Banks have no problem providing these to the account owner, IIRC it's actually required by law.
When he asked for the information or a name associated to the thieving
account, they refused.
There is no "thieving account" here. The transfer was a "push" type transaction. That is, it was initiated from - and presumably authorized by - the sending account. The bank won't give you ownership information for the destination account because in the general case, they don't necessarily know who owns that account. In this specific case they do (since it's at the same bank), but they still won't give it to you. Otherwise, all I have to do is transfer some money to a random account number, claim fraud and get the bank to give me all sorts of information about the owner of that account, and then use that information to help me take over the account.
If this was a "pull" type transaction (initiated by the recipient, like an ACH debit), then you could reasonably say that there was a "thieving account". Banks have a completely separate process for disputing fraudulent charges, however.
In this particular case none of this information would even be useful to you. The target account is likely also a hijacked account, and the money gets laundered through several intermediate layers across multiple institutions to make it hard to identify the culprit.
When he talked to their fraud department, he asked them if they were
interested pursuing the thieving account. They said that was not what
their department did.
Pursuing criminals is what law enforcement agencies do. This type of work requires a wide realm of legal authority and privilege that a bank's fraud department does not (and should not) have. The fraud department's job is to do what they can to prevent fraud from happening, to detect and identify any fraud that occurs, to comply with legal requests from the law enforcement agencies that investigate those fraudulent activities, and to assist customers with going through the bank's internal fraud reporting procedures.
The long and short of this is that you're trying to do the police work yourself. Neither you nor the bank is equipped to do this, from a practical or a legal standpoint. Report the fraudulent activity to your local authorities and let them investigate it. They have experts that can do more in an afternoon than you can do in a month. They also have a wealth of information from other peoples' reports that they can combine with yours to catch the criminal faster. Perhaps most importantly, they have the ability to collect and record evidence in ways that do not alert the suspect and that ensure that said evidence is admissible in future court proceedings. Try to collect evidence yourself and you risk a court throwing it (and the rest of the case) out for some procedural technicality. Police don't always investigate cases like this that involve small amounts but in your case, you already know or at least have very strong suspicions about the identity of the culprit. Report your ex for fraud and forgery, provide the police with all of the information that you have so far, and let them handle it. A copy of that check with your forged signature, her signature on the back, and her handwriting on the front is what the police like to call "exhibit A". The more information you can provide, the more likely it is that the case will be investigated in a timely manner.