I agree with the majority of people that have responded to your post - you need to be very assertive with them and give them a date, soon, to be gone by. Do not fall for emotional blackmail. Just tell them in no uncertain terms that you need them out to prepare the property for sale so that you will get the best price you can in order to move to a property that suits you. Be clear they are not welcome to move with you. Having extra house guests when trying to conduct viewings with potential buyers could be inconvenient at best, a nightmare at worst. What if they are secretly sabotaging potential sales to put their own interests first?
If this is still too subtle for them, tell them that at age 27 he should be more independent and needs to stop acting like a dependent child - he shouldn't need 'babying' as such. If needs be, point out that holidays etc are things people have if they have finances left after paying rent/mortgages and other household/living expenses. Maybe offer to help them budget if they want to tell you how much money they have coming in between them - look mortified and tell them to buck their ideas up - I'd wager they won't want you to know exactly how much they earn, as then you would know how little they have contributed and how much they spend on enjoying themselves whilst freeloading from you and, from the sound of it, expecting free rent and board with chef, chambermaid and waitress services thrown in. It's not on. They need to grow up, and you need to be able to get your home and life back for yourselves. Be ready with positive comebacks for any excuses they try - keep repeating how life can be hard, can be a financial struggle etc - that's the way of the world and they need to pay for their own way in it! Look up storage costs - tell Lucy how much it will cost her to store her crap as you will no longer be storing it for free and having it taking over space in your home - de-clutter, box her crap up if you have to, but better she does it herself, like an adult. She may realise she'd be better off paying rent, on her own rental property, than on-going storage fees! Cut the apron strings or your son will never grow up - you have already gone above and beyond to help them and should be enjoying retirement years, not still parenting a 27-year-old and his partner as if they were schoolchildren.
If that all fails, tell them to fuck off, stop taking the piss, and get back in touch when they have learned to be reasonable adults. Do not back down or the cheeky buggers will be there, freeloading forever.
Hope you have a nice holiday. Good luck with your house-hunting and I hope you don't allow them to prevent you getting the house/cottage you want this time.