Confusing situation

So the long and short of my situation is that I just got out of a very long marriage and I have a young daughter. I met a girl about 10 years younger than me at the dog park. Having already faced the most massive rejection of my life with the divorce, I had no fear talking to women despite little to no practice in decades. Both our daughters were playing together and I cold approached her even though she was on her phone with headphones on.

What took place after that was that we seemed to keep meeting up coincidentally (or not) at the dog park. We talked for hours if you combine all the times we met. I paid close attention to what she said and we both opened up quite a bit about our lives. I wound up getting her number but it was also because I had offered to help her with something and not under the pretense of dating. This is probably where the gray area, situationship began. I really didn't want to do the pretend nice guy act with an ulterior motive.

She invited me to her daughter's birthday party and we attended it at her home. I was essentially a stranger she invited to her house to other people. Either way, the party went well and about 5 days later I asked her out to dinner. She replied enthusiasticly but then cancelled at the last second. But also profusely apologized and said she wanted to make it up to me. We talked until like 10pm that night via text. I went and ate dinner alone which was my plan regardless. I invited her to join me.

I was well aware of the convential wisdom of just deleting someone's number and moving on if they flake on you so early on. But the fact that we had a lot in common, she apologized I figured I'm willing to give someone the benefit of the doubt, once.

I also noticed she stopped coming to the dog park and so I figured I screwed up. About a week later I made plans to bring my daughter to an aquarium for her birthday. I decided to just invite the girl and her daughter and see what happens. Low and behold she accepts, shows up on time, is very friendly and tells me she had so much fun and appreciated it.

I spoke with her recently and her responses via text are more lengthy, enthusiastic and engaging. But she also never initiates any conversations and still never comes to the dog park.

Bottom line here is that there's tons of mixed signals. My dad says we're already dating but I said that's ridiculous because nothing romantic has happened. He said I've already skipped several steps by her being comfortable having her daughter around me and being at her house. He says her cancelling the date was probably a test that I passed since I didn't get upset and went anyway. He says that many women expect the man to do all the initiating early on. My impression is that I just wound up having a play date partner for my daughter and got friend zoned due to not making my intentions more clear earlier on. Any opinions on this rambling story if you made it this far?