K.B.
You say "Its already hard enough to take care of the kids because my husband works and I go to school full-time, so there's only one income in our house." My question to you is why haven't you pressed to make sure you are getting child support? If he is that concerned about his children then he should be paying child support. I imagine if your agreement specifies visitation, it also specifies child support. Most courts allow you to come in without an attorney by filing a Modification Order which would allow you to adjust child support AND visitation to meet your current circumstances. If he lives out of state, the courts will take that into consideration and will define who pays for what. They can also arrange for his paycheck to be garnished for back support. This isn't "money grubbing" on your part or selfish in any way. This is the bare minimum of what the father should be doing for his children. If you let the courts define it then it isn't just you against him. Its an impartial party setting down guidelines in the best interest of the children.
As for sending your 4 year old and 7 year old on a flight unaccompanied, most airlines will not allow an unaccompanied minor under the age of 5 to travel period. So, depending on when your son will turn 5, they can't fly this way anyway. Normally, if he were paying his child support throughout the year the court would say that the father should pay for half of the cost of you bringing them. Since he's not paying, then its not a black and white issue.
This isn't an issue of you not letting him see his kids because he's not paying child support, this is an issue of you not paying for the SAFE transportation of your shared children. I don't think you should have to pay for that. I do think he should have to pay child support. Its not for you, its to enrich the lives of your children. So many women are made to feel bad because they seek the fair amount of support to help raise their kids!