OP - you have made a huge mistake in moving on so quickly with your BF. And people have pointed that out to you - you don't like it, don't like being wrong. Don't like that truth that you have put your children at risk. Don't like people pointing out that YOU have put your children at risk.
That's not bullying you. That is pointing out where you are WRONG! And you have made a mistake!
Accept that you are wrong to have done so, and that you made a huge mistake - and all the advice 'falls into place'.
But you need to get over thet fact that the to-and-fro of who was more mean to whom is irrelevant.
You have gone from an abusive relationship - to one in which you just cannot see the abuse. You can't tell the difference between an abuser who doesn't hit you, and an abuser who is love-bombing you, making himself indispensable, homing in on a vulnerable woman (OR her kids!) , and negging you to chip away at your self-esteem.
One way to find out if he is a 'nice guy' - ask him to leave you alone for a week. No contact, to enable you to think. IF he cries, argues, gets angry, threatens to leave 'forever', tells you you 'can't cope without him' or manipulates you into NOT leaving you alone - this is NOT a nice man.
However, if he IS a 'nice guy', he will leave you alone, do what you've asked of him, wait for you to contact him, back totally off. And let you think about whether you want this guy in ALL of your lives.
My guess? He's one of the former. He's out for a vulnerable woman, to control and use, financially, emotionally, physically. And unfortuantely, the kids will be dragged into it too.