Its a truely shit situation BUT whether he comes with you or not now, it is still not going to be the holiday it was going to be when you booked it.
Things have changed. That holiday you booked does not exist.
What does exist is a fantastic opportunity for you to push yourself out of comfort zone and discover a new type of holiday with your DC. You WILL without doubt come home feeling so much better for having done it on your own. You really will.
If he comes with you, he will be sloping off to do texting make calls etc and it will hurt and piss you off. Create tension and a bad atmosphere. If you get on brilliant when away - you will also feel a double whammy kick in the teeth when you get back to real life and he pisses off back to her upon return. With regards as to whether or not he is still seeing her - does it matter? really? If he and her had split, he has had the last few weekends to make a mends with you and he has not botherd has he? Sorry to be blunt but if he was sure wanted to be with you, he has plenty of opportunity to tell you. This holiday isnt going to change that in reality - and I think deep down you know that.
I appreciate you dont want to hand him 2 weeks on a plate to stay in the Uk with "her" but dont think of it like that. Think of it as being a wonderful chance for you and your DC to have some quality time together.
Personally I would go alone with the kids. However, have you actually asked friends if they would join you? Or have you just assumed they wont because of their family comitments? If you dont ask - you have zero chance of anyone coming with you (thats said I think you would be wise to go it alone).
My kids are 12 and 10 and I have been holidaying on my own with them pretty much every summer since my eldest was 5 due to DHs job cocking up our holiday every sodding year. It can be daunting. It can be scary but you just need to plan ahead and think about how you may now spend the evenings (for example) with the kids and make sure you have water, snacks etc in your hotel room incase you cannot pop out if the kids are in bed before you.
At the ages your kids are - you will have a wonderful time together. If you do go alone with the kids - make sure you block out that this was once a planned family holiday with your H, dont go comparing. Just set out on this new adventure with your kids. Plan with them where they want to go and what they want to see. Perhaps book the trips to the waterparks or where ever. Make it Yours and the kids holiday.
You will without doubt feel so much better about yourself and more confident if you do this.