Reds Field Report - Advise and Comments Welcome

28YO HB7 matched on Tinder a few days ago. A quick back and forth exchange of 2-3 messages, before asking her to meet up.
"...You seem pretty cool. I'm heading to the gym soon, but I'm free later today. Grab a quick coffee or drink with me later"

We met at Starbucks for coffee. She walks up and greets me with a smile and a hug. We begin casual conversation right away, as I order my coffee. She got there a few minutes before and already got hers.

We sat across from each other inside at a table. I made a conscious effort to maintain eye contact, be laid back, take up space. I was able to make her laugh a lot.

Conversation began with talking about our daily lives, schedules, why I chose the career I chose.

Unfortunately as the conversation unfolded, talking about where I am from (I currently live in midwest, but am from Florida), took a turn to discussing family. At this point upon reflection I feel the conversation became very predictable, and less fun. I feel like I should have redirected the conversation towards more fun and exciting things, such as asking about hobbies, things she likes to do, or telling her about some of my interests.

I should have probably worked in reaching across and touching, or holding her hand across the table early on. I have been able to seemlessly weave that into the context of the conversation most of the time in previous dates.

I've had success at getting a lay when meeting a girl from tinder at the same starbucks. So I though the move was to change the scenery. So it didn't feel like we were interviewing each other. So I suggested we go walk around (Starbucks is part of a mini outdoor mall like area). I was hoping this could inject more energy into things, and perhaps steer the conversation to something more exciting.

Also since I didn't reach for her hand, I thought it would be easier to grab her hand to hold it while we were walking. At first I was on her right, but her purse was on that side. So I made a quick move to throw away my coffee cup in the trashcan, and repositioned myself on her left side, however she was holding her coffee cup in her left hand. I tested out some around the shoulder hugging and minor touching as it came natural in our conversation. There didn't appear to be any resistance, but she also didn't lean into me during those instances.

The conversation still remained on family, her job/my job, her kids. I was probably too much in my head at this point because it wasn't going the way I wanted. I was too busy thinking how I could steer the convo back into something more cool/fun, and perhaps create some sexual tension.

Before we met, she told me through tinder she had kids, wanted to be upfront. Said she was only free before 4 pm. She checked her phone on average about once every 15 minutes during out 1.5 hour long meetup.

Although I didn't feel like I had enough positive IOIs to try to pull her to my apartment, I was still considering going for it. I figured she could still agree or in very least it would cause her to shit test me, for which I had planned on being calm, alpha, and collected and breaking through, which may lead to her becoming sexually interested. I took a quick glance at my watch, that she didnt notice, it was around 1:55pm. I admit I hesitated a good 15-20 minutes by not asking her back to my place. The conversation was mutual still, and I was hoping to try to turn it into something more fun, before going for the kill.

That 15-20 minutes passing did not seem to help, so I was just about to [honestly I was, not being a keyboard jockey here] say something like, "So, I know you said you were going to be busy after 4, but how about we swing by my place so we can relax and chat more, Maybe put on a movie." (earlier in convo I had mentioned I lived right across the street from the starbucks/mini mall).

She then blurted out, "Well I think its time I need to get going. My ex is asking me if I can pick up the kids today, and they get off at 2:45." I acted outcome independent, calm and collected I said okay. We continued chatting for another few minutes walking to her car. We then were joking about her poor driving skills she had mentioned earlier in the conversation. We were both laughing, the vibe was weakly positive/upbeat. Certainly not awkward.

She then said "alright, goodbye", and reached out for another hug, so I gave her a hug. As she was leaning back from the hug to look at me again, I held her waist, and looked into her eyes, and moved my face ever so slightly closer to hers. Not hugely obvious or over done, but enough to communicate with my body language I wanted a kiss. She said "No kiss on the first date!", I laughed it off, but, I could have probably done a better job holding frame. I'm sure I did subcommunicate a hesitation, or momentary lapse in frame.

As she was closing her door she said, send me your number through tinder, said our mutual goodbyes, and she drove away.

I waited about 40 minutes, I reasoned I don't want to respond too quickly, but I also don't want to take so long, that she may assume I am a little bitch beta male who has run away with his tail between his legs. I simply said "XXX-XXX-XXXX shoot me a text so I have your number also". I didn't say nice to meet you, or look forward to next time. I figured that was too beta.

My thoughts are
I either wasn't aggressive enough to cause that sexual attraction to happen in an alpha fashion, and missed the boat, and along with the boring joe-smo conversation we had, she probably lost interest.
Or, along with the above, I communicated not the 'alpha male, guy expects sex because he gets sex' vibe, and portrayed a more beta 'well, in a year hes going to have an extremely high paying job, and he could be boyfriend material, but not fuck on first date material. Maybe I'll fuck him eventually, if he wines and dines me'.

Being overly optimistic, the third possibility, is that she really did have to go pick her kids up early. She has more traditional values, that I didn't overcome with my beta behavior and conversation, but she is interested enough that on a second or third date, the sex may happen. Upon reflecting after/while writing this post, I feel pretty strongly from the vibe I got, that this is very unlikely [and thats okay, I got to talk to a new girl and practice chatting, I'm still upbeat, and not affected emotionally]. Its not my plan to spend a bunch of money on her, if she won't give me sex first.

Appreciate the feedback.