Do you have a lawyer? Is there any sort of 'emergency' motion that can be placed before the court for it to rule? I agree that most issues take months to get before a backlogged court and even more months to resolve, but is she was previously agreeable and now refuses, that may be basis to ask the court to intervene.
Perhaps you can ask the court to order the the passports held in safekeeping and allow fair use to both parents? Understand that you may need to post some sort of bond or assurance that you will bring the children back.
Even after separation BPD was telling children l was going to take them to live overseas which is not true as this country is the children's home and always will be... . Now BPD is refusing to give passports as is using them as Leverage over financial settlement... . I feel BP is trying to break me... .
Ah, Leverage. Has she has offered to release their passports IF she gets her terms? The court may frown on such tactics to sabotage an already-planned and imminent trip.
The problem with a "settlement" is that if she is still too entitled or controlling, a settlement will either fail as unreasonable or you will hand over more than you should. Odds are that you will regret sacrificing too much for this trip.
My story... .I had gotten my Final Decree over a year before. School's Winter Break was approaching and I saw that if I declared a week's vacation I could have nearly 7 days between Thursday 9 pm and the next Thursday 6 pm, the time between Christmas and New Year's Day. You can guess, she said No. (It was a notice, not a request, after all.) Well, she then claimed she wanted to observe Kwanzaa (never observed before but it did appear on the county's list of holidays) which would have cut my week vacation nearly in half. She successfully sabotaged me, I cancelled. But later in court she testified she knew Kwanzaa involved candles but she still wanted to observe it even though she wasn't of Jewish Descent. My lawyer had a field day asking her for more details about this Jewish holiday. Her lawyer couldn't intervene without highlighting it wasn't a Jewish holiday. Finally the judge asked him to move on. It was that part of her testimony that the judge's decision called "not credible".
Another tactic I learned was to schedule my vacations to start on my weekends. One time I served my ex with a Notice and her response was, No. (So sorry, it's a notice, not a request.) I had thought ahead and scheduled it to start on my weekend. She's couldn't complain to officialdom until my 'weekend' time was over. Police called me but said it was out of their hands. She tried to get an Amber Alert on me but the nice deputy sheriff correctly and politely told her, "It doesn't fit the criteria for Amber Alert." She demanded an investigator, the investigator called my lawyer (who had told me to have a great vacation) and so my lawyer called me and told me to have my son call her every few days. I said she can call our son anytime. He knew she wouldn't, so just repeated to have 4yo son call her.
I tell those events to help you overall for future planning, even if they don't help you in the current pressure of her withholding the passports.