Were you paid to drive that van ? If so, that is commercial driving experience ! That is their problem if they didn’t define what they think commercial driving is - A CV would clear up any confusion for them anyway.
I understand you’ve also moved a neighbour/mate’s old horsebox around too? Non-Commercially ofcourse, just as favours
You’re going to need to stretch, not break the truth a little to get your first Class 2 driving job.
Good Luck !