It is a tough situation.  Your children are caught in the middle.  Since I don't know how old they are or the circumstances of the threat of abuse, it makes it difficult to answer.  

You said that it was two years ago that your youngest said she misses her father.  Has she said it since then?  If so, then I think you need to address her feelings.  Talk to her about it.  Ask her questions that encourage her to open up.  Be honest with her, but she doesn't need to hear all the details of why you two are no longer together. Does she even remember the incident when the abusive threats were made?  What is it about her father that she misses?  Once you know more about where your children stand on the issue of their father, you can make better decisions.

You always need to consider the safety of your children.  If you believe they are not going to be safe if they spend time with him, then contact your lawyer to see what kind of options you have in keeping your children from seeing their father.  

If you believe that nothing will happen as long as you are near by, then maybe you can set up a meeting in a public place - some place where the kids can see you and you can watch to make sure they are ok.  This might be a park, restaurant, or movie theater.  You can make the meeting short and sweet.

You may also want to look into counseling for your children so they can learn to deal with their feeling towards their father.  Most communities provide free or low cost support groups for the children dealing with such issues.  Some religious organizations also have groups for children or even the whole family.  Also, check to see if your employer has an employee support services - usually part of your health care plan.  They can set up with the therapy for your children.

It sounds like you will need professional advice from a lawyer for the legal questions and a therapist for the emotional needs of your children.  As a mom, continue to give them lots of hugs and kisses.  Talk with them, one-on-one and well as a whole family.  They need to know that you care and are doing what is in their best interest.

Good luck!