Ohh man, this sounds soooo familiar. We are going through similar issues with my husband's ex, she's $4k past and never shows up for visitation at the last minute, then accuses him of trying to keep her from her kids.
(EDIT: I typed out the following, and missed the part in the original post that implied there's no parenting plan in place. Obviously, the following only applies with a parenting plan, but it could still be helpful info for you in the future or someone else, so I'm going to leave it - also this is all for the state of Washington, but again, might be helpful)
We've consulted with a lawyer, and I'll tell you what we do know as a result. I'M NOT A LAWYER, so please take this all as one person's opinion, everyone!!!
1. Child Support and Visitation are two separate issues, and visitation can't be held due to lack of child support. They are handled with different forms/legal proceedings etc. If you don't let him see the kids because of back CP, YOU can be found in contempt of the parenting plan, and if he really wanted to he could raise a stink about Parental Alienation and get you on this.
2. If he's back in child support, not only can you have the state start collections if you haven't already (although if he's like my stepkid's mom he'll job hop so that they can't garnish - its amazing what people will do to avoid their responsibilities) you can also file a petition for contempt - he's willfully ignoring his child support payment, which is a disregard for a court order. This can't magically make him pay, but it may show him how serious this is, how serious you are about wanting him to take care of his kids, and it will go on his permanent record, for your divorce/parenting plan. That way if you need to fight in court about things later, he looks like a big old irresponsible parent and it helps take steam out of whatever he tries to convince a judge that you are doing.
3. What the parenting plan says about visitation you're legally bound to - i.e. if it just says he gets first and third weekends and he knocks on your door to pick them up, you legally have to hand them over, or face potential contempt yourself. However, if your plan is well organized and says "non-custodial parent will pick up the children within 1/2 an hour of 6pm on the first or third weekends of the month. If the non-custodial parent doesn't arrive or call by 1/2 hour after 6 pm, their parenting time is forfeited." It's not hard to get a change/modification like this, because it just clarifies, doesn't really remove any potential visitation, and yet holds him accountable. It's intimidating, but you can do it!! Protect yourself on paper!
4. As far as emotionally protecting your children (and this somewhat depends on his ability to not mess with their minds when he DOES call/show) in our home we don't tell the kids its their mom's weekend, or mom is planning on picking them up. Because 99% of the time she just never shows, and they would be devastated if they knew that. They are blissfully unaware. If she does show, we go "SURPRISE! Mom's here to see you!!" and then they go off for what's usually a measly 2 hours instead of a whole weekend. Maybe you could convince him (rightfully so) that it upsets the children emotionally when he doesn't show, and to just work it like that to help them stay more emotionally balanced.
This is a big slice of hell you're living, there are so many more of us out there doing it too. You're not alone!
Please PM/email if you need to vent/discuss more.
Good luck!!
~S.