I'm on the fence. Hope you will allow me some scope to explain.
the sitting on the lap thing - I've done it, I've seen friends do it and my sister-in-law does it with her Dad (my FIL) but context is everything.
Trying to think of an example to give the context, so on holiday - we were once taking the piss out of my FIL. All good fun and some banter. It was his birthday. There'd been some alcohol. There'd been some attempts at doing a tik tok dance. It was a good night. My SIL sat on her Dad's knee and did a 'oh Daddy we do love you really' with her arms round him. I have a photograph of it. She was 30yrs!
So that's the sort of time and place where I've seen it/done it.
If my FIL had a new wife at that dinner/evening - I could imagine her being a bit put out by it. Of course, her own Mum just laughed and said - 'oh here we go, fluttering your eyelashes, what are you creeping for? What you after?' Said as a joke, like going back to a time when the 6yr old version of her would do this.
The other point is it could be that the daughter feels highly insecure of you.
I had a friend at uni who was in a similar situation and this might be quite relevant to you. Her Dad remarried a few years before she started uni and everytime he came to visit - she threw herself at him and was so over the top with the 'oh Daddy, haha. Daddy you're so this, that and the other' Cuddling him constantly. It was weird.
She got really drunk one night, wound up breaking down about how no one loved her. She also didn't have a Mum in the picture (think she moved abroad). Basically her lifestory was that after their divorce - everyone had moved on with new lives and new families and she just didn't know where she belonged. She was desperate to be someone's number one priority. She was howling, took 5 of us to try and calm her down. It was all no one loved her. No one cared about her. It would be easier for everyone if she was dead - that sort of drunk emotional breakdown. She didn't have any biological siblings either, although all her step-siblings did.
Away from her family dynamics (and alcohol) she was smart, confident and self sufficient. Although it was clear there was something off with her - she was running a bit of a personality disorder that would be too long winded to explain here. But something definitely not right.
She graduated uni and I heard some years later she had a complete and utter break down - she had to go to a sort of priory type place - as in - she wasn't sectioned but she was hospitalised for it.
So perhaps she's deeply insecure about you. Her own mother clearly doesn't give a stuff. You have your own kids, plus you have her Dad.
Your gut might be right - something is off - but possibly you're a bit off the track about why.
Maybe read up on attachment issues - that might help.