Glad you can dress it up as a mini break. Heart breaking about oldest he's probable missed his dad and believed him coming home would mean time together , then he spends most of time doing his own stuff.
Think once he's gone and you back home then tell kids truth, I woulnt risk it now incase the kids say to him and he kicks off. But you had time discuss this as family and approach telling kids, if he can't accept that then to late now.
Maybe worth ring to benefit office see about claim it's been 3-4 weeks now? Hopefully start payments before 6 weeks.
He may well feel embarrassed with family and friends but he's not doing anything about it, because disclosure and money are more important than you and kids.