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What province is this please?What is the father's income? What is yours?
If the children live with you for at least 60% of the time then he has to pay child support based on the Federal Child Support Guidelines. At $27K he only has to pay $427 a month but if he is really earning more and you can prove that then the court will impute income to him and require he pay more.
It is hard to see how his income is that low and yours is $40K and the kids went to private schools so you can likely easily prove his income is much higher.
You cannot force him to have shared custody and pick up the kids etc.
It is not likely possible to have the court say funds have to be put in trust in case he takes off.
It doesn't sound like you should be agreeing to anything at this point as his dishonesty about his income is very troubling. If he income is higher than yours would be entitled to spousal support as well potentially.
So what you really have to do is have a lawyer go over his and your financial statements and discuss how you can show what his income really is as you are not going to get a fair deal if he is lying about his income.