You need to look up the laws/guidelines in your state. They should be available online, for free. Here, for example, we can search for "Indiana Child Support Guidelines". You might try a similar search.
In MY state, if a divorced couple already has court orders in place; if at least a year has passed since the most recent child support order was issued; and if there has been a substantial change in circumstances, either party can pursue a child support adjustment through the child support collection office, without going to court. In some jurisdictions, child support is a straight calculation of who makes what, how much time the kids spend with each parent, who pays what for childcare/health insurance, etc. In such a case, your DP might be able to adjust things so his ex pays C/S to him, just based on all of those facts. However, it may be necessary for him to petition for an official change of custody - to reflect that the kids now spend the majority of their time with him - in order to reverse the flow of child support. That would involve going to court. You need to read the laws, to know.
If you (of course, I really mean HE) wind(s) up in court, it's certainly safest to use a lawyer. In fact, if he already has a lawyer representing him, he must file something with the court officially terminating that representation, in order to represent himself. And it's possible his attorney or the judge might give him flack about that, if he still owes his lawyer money.
But if you can't afford to use an attorney, more and more people are representing themselves in court. It is possible, especially when the facts are not in dispute. So, if your DP's ex will acknowledge how much time the kids spend with you guys; and everyone agrees how much everyone else makes, then you're really just asking the judge to decide what's reasonable and sanctify it with a new order. But if she claims the kids are with her 5 days a week, then you guys would have to subpoena her work records; and people to testify about her hours; and then put her on the stand to ask, "How can you claim the kids are with you this much, if you're working these hours?" In that case, you're really better off with professional representation.
But overall, this sounds like an issue that's on the easy side, compared to other things people fight about in family court. It's all pretty objective. If she works for a hospital, there are records that show how much she makes. There should be paperwork showing how much your DP lives on. A judge may be willing to accept that he's not capable of working; or, worst case scenario, a judge might calculate C/S crediting your DP with having the potential to earn minimum wage. But even so, if his ex out-earns him; he pays for childcare (and there should also be records to substantiate that); and he directly provides for the kids' needs a clear majority of the time, it should be fairly simple for a judge to conclude that she should be the payor now, not him.
If your DP's going to pursue this, he should also check into health insurance. (If you mentioned it in your post, I didn't catch it.) If she works in a medical field, she likely has access to coverage for the kids. The court might order her to provide it and a National Medical Support Notice could be sent to her employer. Payment for the kids' policy would be withheld from her paycheck, eliminating the possibility that she'd terminate insurance one month because she was mad at your DP, or just having trouble covering her bills. Of course, what she paid for the kids' policy would be credited to her, in the C/S calculation. But, your DP is mainly looking to reduce how much he pays her, not so much to have her pay him as much as he can get, right? And if health insurance for the kids is an option now (perhaps it wasn't, when he was unemployed and she was a student), it's responsible to try to make sure they have it.
Your DP's ex will likely feel very threatened by all of this. Understand, from her perspective, your DP will be "trying to take her kids away from her"; trying to take away income she has come to expect; and trying to make HER pay things she will feel she can't afford. It may be valuable for him to try to talk with her in a civil and compassionate way - BEFORE she gets served with court papers - and explain that he doesn't want the kids to spend any less time with her than they are; he doesn't see her as being any less important to the kids than she always has been; he just needs their financial arrangements to start reflecting the changes in their schedules, because he's really struggling. She may not be receptive or respond well to this, now. But if your DP handles this as kindly as possible, instead of just blindsiding her with a Petition for Modification of Custody, later she may be able to realize that he wasn't trying to "screw" her; that it really wasn't reasonable to expect him to keep paying the same amount, after the kids started spending so much more time with him.