So Dad asked daughter if she had her stuff.
She promised she did -- but she didn't.
In raising children, the right answer is almost always NATURAL CONSEQUENCES.
In this case, having neglected to pack all her gear, the natural consequence should have been that Daughter didn't swim that day. This was swim team practice? Her coach might've told her that she couldn't participate in the next meet, might've made her run, or whatever. If her mistake hurt the team (i.e., if she's part of a relay team), the consequence might've been that her friends were angry with her. That should have been HER RESPONSIBILITY. Dad should not have "saved her" from her mistake. He should've allowed her to learn from it.
Thing is, the same NATURAL CONSEQUENCES works for Dad too. He bought a new (and rather expensive) swimsuit for Daughter rather than let her miss an activity on his watch. Now the natural consequence of his choice is that Dad is out $40.
If Dad chooses to push the issue with Daughter, let that be his choice. Your best course of action is to do NOTHING. She made the mistake, and he made the choice. You were not involved. Do not involve yourself. If your ex-husband pushes it, say honestly, "I wasn't involved in this situation. You two need to work it out." You are not undermining Dad's discipline, nor are you telling the child she essentially doesn't have to do what Dad says; rather, you are staying out of an issue that occurred between the two of them.
Another NATURAL CONSEQUENCE might be that she needs to spend more time packing her swim bag. Perhaps make up a checklist and have her give up a few minutes of free time the evening before a practice, then show it to you so everyone knows that this problem won't repeat itself.