Sorry I didn't mean to quote this and can't edit it out!
The ones who burst into tears are two eight year olds who were feeling responsible for adult emotions (their dad said it would ruin her weekend to admit to her how they feel - how did him even saying that to eight year olds come about? They should not be pressured into taking responsibility for their mum's feelings nor especially into keeping their feelings secret).
I don't think the OP has mentioned an adult girlfriend being involved in babysitting or indeed present over the weekend, that's a misreading that has been repeated.
There will be the half brother who doesn't live with his dad and sees his half sisters only when he visits his dad on the same day as they do, which OP said was once a month, and there will be the dad's girlfriend's son who is 18 and the OP has never met - he is the one who lives in the house.
My personal concern before hearing the younger two don't want to go was that the 18 year old will end up with friends over - possibly even without having planned a "gathering" or house party. He's got a parent free house for the weekend and only his mum's boyfriend's kids about.
Over the summer my 17 year old son has been going to lots of "gathering" type "not a party" meet ups at whichever friend's parents are away (I usually pick him up if staying over isn't an option because we're rural and several miles from the nearest public transport stop, and as his school catchment was massive some of his friends live 20 miles away on the opposite side). Driving home, having had a few beers, he tells me funny anecdotes and an upset small sibling the friends didn't realise the host had/ was home turning up in the midst of the late night teen revels in his pyjamas has featured once. Nothing bad happened but it's not ideal...
The 20 year old who has no experience babysitting being chucked in at the deep end babysitting three children he's never lived with despite the half brother relationship is already not ideal. Two eight year olds who want to be elsewhere plus an eleven year old who's at the age where it's normal to be a bit stroppy OVERNIGHT when he has never looked after them or any child before is a lot. My eldest used to babysit and sometimes the preteen siblings of the children she was primarily babysitting were more challenging than the small children behaviour wise, trying all sorts and claiming their parents allowed it - fortunately she has younger brothers and was wise to it...
It's really quite disingenuous to claim that eight and eleven year olds are practically capable of being left alone and no trouble for someone with no experience of looking after children, who hasn't lived with them as a sibling either despite blood relationship, to be in sole charge of for 24 hours.