@IvanovaG
Hi i used to work in housing law but not a solicitor.
There is no such thing as squatters rights in private homes there is legislation about this.
Your daughter and son are technically living in your home on an excluded licence which means you can tell them to leave, and place their belongings out on the street and lock them out with minimum notice say 24 hours.
As for the boyfriend he is a lodger, his payment to you is not a gift it is “room and board”. He is also on an excluded licence so the same as above applies. You can just tell him to leave and throw him out.
The risk that you are implying here i think is that you may be locked out upon your return from being away.
If you own your home then that is not such a problem as legally you can break back in as i assume that you can prove that you live there.
If you are renting you could have a problem as the boyfriend could argue to the police that you sublet to them (produce a fake tenancy) and state that you don't actually live their in which case the police might say it is a civil matter.
if that happened you would have to go to court to evict him/them, and you would have to find somewhere else to live for probably a year, whilst paying rent for them.
I have no idea why you would allow the boyfriend to continue to live in your home given his attitude, and assertions and it sounds like he is manipulating your vulnerable daughter.
What would i do if i were you?
I would not go anywhere until you have chucked the boyfriend out and ensured that he is excluded from your home in writing and keep a copy.
if your daughter goes with him so be it. You are being emotionally blackmailed.