I think you may want to have your husband be the main communicator...he's the one with something in common (the kids) with her...you more removed, so it will be less effective if you continue to communicate with her.

I really didn't follow the mention of an investgator other then to understand there was no child neglect/abuse.

If you were reported and it wasn't substantiated it would suggest that kid's mom is a bit toxic for you guys, so think about how you will limit exposure (these are the things that will start forming your boundaries).

For example: You and your husband may want to decide to limit all communication to ex to only subjects that involve the kids they have in common...and the only communication/decisions happens first between you and your husband and then through your husband to the ex and vice versa...so if ex asks you to make a decision you can either redirect her to your husband or let her know you will pass on the information (then you and your husband can make a decision and he can get back to her)

Does this make sense why I might suggest this?