You are gluttons for punishment
Girl teens are complicated and yours sound typical
At their age I didn't want to go anywhere with my parents nor did my daughter
Could it possibly be you have an ideal vision which unfortunately they do not hold ?
It's possible that nothing you do could make it attractive.
On a more positive note we took our truculent spoiled 13 tr old to La Quercia an all singing and dancing Lake Guarda campsite where attractive young people are PAID to engage them in activities day and night. They only report to you at mealtimes/ bedtimes.
It worked a treat - not really our cup of tea but hey ho if the kids are happy everyone is happy.
We went for years on the run and eventually she to a summer job there
Time marches on 15 yrs later we still go now as large family groups and madam brings our gorgeous grandkids.
We once took her to Verona and she spent the entire time skulking in McDonalds
Good luck- be careful taking a mate it can cause double trouble