You can cancel the automatic transfers on ING you know. Automatic doesn't mean autopilot, it's important to monitor these things. I doubt they will give you back the money another bank charged you, it may be better to go speak with someone in-person at the bank that charged you the fees. In addition, you may be able to contact the companies (who may or may not) have also charged you fees for a bounced check.
Best of luck. I know everyone can't monitor their accounts daily, but I have alerts set up so if say a withdrawal of over 100$ comes out I get an e-mail (which I do check daily), or if my balance dips below say, $300. Nearly every single bank, especially online banks, have this feature.
It may be better to do one-time transfers, instead of automatic transfers. I ran into a similar issue transferring from checking to savings, but within the same bank.