First of all, you have two beautiful children. Thank you for reaching out, so you can get them the help that they need.
Second, it's important to recognize that your children have been abandoned by their father and they are victims of those feelings of being left behind by someone who was supposed to love and protect them. Despite this, you need to do all you can to get them back on track, so they can lead happy, productive lives as adults.
Third, your children don't believe their birth father loves them because he is not in their lives. If he loved them, he would do everything in his power to spend time with them. Don't make up stories to make your kids feel better, instead, teach them how to deal with reality.
Fourth, it sounds like your son might have a conduct disorder. Don't feel bad if your attempts at discipline have failed because parents of such children need to use different strategies than their parents used.
Understand that you must take action now because if you allow your son's behavior to slide, it will get worse as he becomes a teenager and the hormones kick in. I recommend that you get your son into therapy or use the Total Transformation, a behavioral change program that was designed to show parents how to turn around their kids. This program is will also benefit your daughter and is geared to kids with a conduct disorder. The key is to listen to the instructions and apply them. In order to change your kids, you need to change how you interact with them.
Although it might be hard at first, remember that by turning your kids around, you are quite literally saving their lives. After all, you don't want to end up like their birth father, in and out of jail. I hope this helps you and your family.