Yes, judges may modify their own judgments on thier own motions (in latin lawyer-speak we say "sua sponte"). It's not uncommon.
You say it's "obvious" that her attorney contacted the judge. What makes you think so? On what facts do you base your suspicion that your former wife's attorney has had ex parte communication with the judge?
Finally, do you have some objection to paying the fees you were ordered to pay? Were you planning on discharging the fees in bankruptcy?
What would organized religion be without hyper-technical restrictions enforced by an unwavering hierarchy? No shellfish, no cattle grazing with other kinds of cattle, no hair braiding, and absolutely no headstones 2" too short.
Write to Cardinal George. Try to get an agreement before taking matters into your own hands.
Failing that, if they come after you, remind them of the Church's robust history of recognizing wrongdoing, and working with the law to seek justice for wrongdoers....
The pool / park / jumping business is ridiculous. When your child is with you, you're the parent: you make the decisions. If Mom doesn't like it, too bad. End of discussion.
On the "I-have-to-work-during-my-visitation-time," I think you've got a slight exposure to a small problem. There is an argument to be made that a child should be with an available parent rather than a care provider (like, a grandparent.). The language in your order probably doesn't deal with this issue.
You CAN'T ensure that on your return your ex won't claim rights to their custody. Any agreement you might reach would not be enforceable if she went to court to seek to modify custody. The court will not be bound 26 months from now by an agreement reached today impacting the children. Indeed, when it comes to kids, courts are NEVER bound by the parties' agreements.
Your attempts to paint her as a less than desirable parent (she's not as financially, morally, or emotionally stable ass you)...
There are a few things you can do in an effort to derail the divorce train . . . filing a counter-petition is not one of them. Neither is filing an Answer. You need legal help. You should call an attorney who can help you fight the divorce. Below is a link to an article you might find helpful.
First, Your problem is only 16% of the ruling and, by definition, it's only temporary, so let's not get too worked up and talk appeals. The child support award (roughly 2/3 of the award) is nearly always determined as a function of your income without much consideration of your wife's financial standing. Second, you don't reveal other factors that very well may have warranted the judge's ruling notwithstanding your wife's non-compliance with discovery (for example, if you packed up and moved...
"Entitled?" No; you're not "entitled" to anything.
Presumably the interest is marital property so, you should be able to take some share of it: maybe half, maybe more, maybe less.
You need an attorney.
Below are a few links you'll find informative.