Get yourself to a lawyer ASAP. That veiled threat that she could take the kids to Hawaii? You need to speak to a lawyer about whether there is anything you can file right now to prevent that.
Mediation can be a good idea - IF the other party is capable of being reasonable. In my divorce, we had a mediator, and then we each had our own personal attorneys that we consulted with on the side. This was important because my own attorney could give me a perspective on what was reasonable and what would be unlikely if we went before a judge.
Do you have some idea of what she is going to be requesting for custody? Maybe she wants to have the kids for the whole summer so she can take them back to her lover in Hawaii? (Or wants YOU to have them for the summer so she can do the same unencumbered by children?) Maybe she wants full custody so she can get maximum child support as financial reality is sinking in for her?
Either way - see your own attorney ASAP, and use them to advise you through the mediation. keep the emotion out of things and just look at it as a business transaction (which it is - a very important business deal).
