I would ignore your parents OP, they just sound spiteful. By 19 I was living at the other end of the country and pregnant ... by 21 I was living in a totally different European country with my DD and my Ex.
I work for a company that runs teen summer camps and earlier in the summer 70 14-18 year olds were left in the care of 6 22 year olds for a fortnight. If they can watch 70 teenagers at camp, a 19 & 21 year old are more than capable of watching a 15 & 13 year old in their own home!
I would however use their threats to prepare your boys for any issues that might occur while you're gone and what to do in those instances.
Inform their school that the younger two are being looked after by their brothers while you're away and give them their details in case they need to get in touch with someone (or if your parents call the school to cause trouble they will be pre-warned)
I'd also make sure they have a friend or someone to call in case of emergency that knows you will be away and the situation with your parents, just so they can call on another adult's support (eg if your parents come round or the police turn up and they feel out of their depth, having a family friend on speed dial may reassure them.)
I'd make sure the cupboards were stocked with the basics, make sure they have money for groceries/petrol (if one or both of the older two drive) and maybe leave an extra £20 takeaway fund emergency fund just in case.
I would also leave your itinerary with them - what hotel/resort you're staying at; it's address/phone number; your flight details so they know when you'll be gone & when you're due back. Again, if the police do get a call and show up, the fact that your kids have the info (and you have a return flight!) shows that they haven't been abandoned and they can contact you if needs be.