Hi there! I'm sorry to hear that you're struggling to find a holiday that fits your family's needs. It can be tough to find accommodation that can comfortably accommodate a larger family without breaking the bank. Have you tried looking into all-inclusive resorts that offer family-sized suites or villas? That way, you can have all your meals provided and still have plenty of space to be together.
As for warm destinations outside of the UK, have you considered Spain or Portugal? They're both popular holiday spots and have plenty of family-friendly options. I hope that helps, and if you're looking for something really adventurous, check out these Kilimanjaro tours: https://altezza.travel/en/kilimanjaro-packing-list