Have now read all posts from this morning.
Yes, he needs to sort himself out emotionally to let his little girl grow up. He also needs to help his daughter feel secure, happy and loved by him. Physical contact is her claiming possession of him (jealous of the OP) as well as needing tangible evidence dad still loves her and she is still important to her and his number one priority which she is and should be forever. She is away at uni and gets the love from a distance but needs to feel it is real and needs to see it. she also needs to remind you of it, by clinging on and showing you.
I also want to know how Op's 5 year relationship is going with DH- he does need to ensure OP also don't feel unloved or competing for attention.
ONE important this being hugely overlooked here, although mentioned by 1 or 2 pp is the age at which OP met DH. She was 14. For 14 years she only had her dad in a very intense and hugely relevant way for them both. Hence both need help to disentangle.
Other good advice given already,
However, seeing the dynamic, I would NEVER broach it as her needing to make her own decisions (dad will say you are jealous and I know many men who are so weak they will drop you in it if the daughter questions why the change). BUT I would take the opportunity of strangers mistaking her for his GF like a shot and start a convo. OP needs to bring it up but saying it is other people saying it and then offer advice of stopping lap sitting and hand holding when at home etc etc.
I also doubt daughter is clingy and holds hands with dad when it is just the 2 of them- this I would ask DH. Of course she might still do it when your sons are around, which speaks to her jealousy.
You love them both and you care about them both. Be sensitive as you have been and I am sure you will help them both positively.
Yes, upper class and wealthy families are like this: just not sitting on laps too much (pp here gave occasional scenarios or when having a panic which are isolated and particular events); and not holding hands too much. Personally, this would always be my starting point: my niece and her dad are close (no sitting on laps, no emotion or hand holding). I was also close to my dad- he died when I was 12- also no holding hands, sitting on laps etc. My brother assumed father figure and we have remained close. I now see it has helped I moved countries at 27; I have known his now wife since we were growing up; as he is way older, I had not needed to run all my decisions past him but I did value his advice as he is very well-rounded. Also we were 5 siblings and mum and cousins so I wasn't only just reliant on my brother for support. She only had her dad and still only had her dad.
I am very sweet and empathetic: When she says she wants time alone with her dad; I am likely to respond that ; 'You are welcome to have lone time with dad anytime. I am off to sort my wardrobe as have been procrastinating; or I am off to the gym as need to go'. But I am truly independent and that would all be true. Once she sees you are in no competition with her, trust me, she will let loose of dad.
Also, take it as a compliment that she thinks you are perfect and her dad is very happy with you and loves you. That's why she is reacting in a needy and clingy way. @VivienneBMama Good luck and take it easy!