It is wild to me the number of people being blamey and judgemental to the OP here. She has admitted herself that she didn't cover herself in glory in the original argument. However she did not commit physical violence against him. She threw a baby's hat. It's not great, it's not perfect, but she was tired stressed and in charge of 3 of THEIR children (not 'HERS').
And for this 'crime' she has been abandoned in a foreign country with 2 toddlers and a baby on her own. And crucially, even if one were to accept the OP is at fault which I do not then he has still abandoned his children whilst on holiday. What an absolute complete and total knobhead.
I am a bit too impulsive and can be stressy and snappy when I'm tired - it's not great, I work on it as best I can. I can just about imagine getting to the point where I started to flounce off in a reverse situation. However I wouldn't get to the end of the corridor before realising how wildly unreasonable and disproportionate that would be, turning around and coming straight back again. As a PP has said, this type of bickering happens when both parents are tired and under stress. There's some excuse for it. But seven hours is way too long to need to come to your senses. And it seems it's a pattern of behaviour.
Personally, I think booking the flights tonight for very early tomorrow morning is unwise as it'll be another night without enough sleep for everyone (even ignoring Dad coming home in the middle of the night and waking everyone up) so I think it'd be better to just try and get some sleep and have an attempt at sorting out the relationship issues enough to limp on with the holiday and salvage something from it, not least by leaving all 3 kids with him for at least a day to get some time to yourself, OP. However if he's still - somehow - in the same mood tomorrow then you know where you stand - book another flight and get the hell out of Dodge.
And I also think it's interesting that friend is willing to lend you the money so easily - presumably friend has seen this before...
Good luck, OP. I hope this turns out better than most of us fear.