I’m not sure what your affect your past will have on a custody case. I do not believe that a charge without a conviction can be held against you in this situation. I’m not sure the judge for custody could or would be able to “hear” this in court since the issue itself hasn’t gone to court. This really has no merit on your ability to care for your child or what kind of parent you are either. I believe that you are being intimidated.
The best thing you have done is to keep records as you have. Make sure that the courts know if you are willing to settle for joint custody with equal time but that his history with the child shows that this is not what he wants. If the judge does find out that he’s going for custody simply to reduce child support instead of for your child’s best interest he/she will not be pleased. Trust me.
I won’t tell you that you have nothing to worry about because the courts can do anything and sometimes it seems there is no rhyme or reason. But I can tell you that if you do have a good lawyer, you have kept good records, and your child is well taken care of while in your care…that will speak for itself. The threats are a bonus that hopefully your attorney can get admitted to show that he only became interested in custody after having the courts mandate child support and that he has been since trying to get you to let him pay less…
I think you should be alright.
Keep us posted and Good luck!