My (43M) girlfriend (46F) seemingly and abruptly ended our relationship and the reasoning has me confused. How do we move forward?

We have been seeing each other for roughly six months, talked for about three prior to that. Because we both have kids (she has two and I have one) that still live with us at least part time, we took things very slowly before applying a label (we were together for four months before our kids met each of us). As far as I knew, everything was going ok despite a couple minor hiccups that we encountered. We spent the entire weekend together, both with and without the kids, I met her brother and mom for the first time last Friday and we spent the night Monday at the pool together with all three kids.

The first hiccup was a couple weeks ago when she invited my daughter (10f) and I to the rodeo. I wanted to go but my daughter decided she didn't want to (had just gotten home from a vacation with her mom), so I declined the offer. My girlfriend seemed to take this more personally than I anticipated. I still regret not going. The second hiccup was apparently Tuesday when she asked if I was going to fly down to meet her and the kids on their vacation next week (she offered to pay for the ticket). I am covering for a coworker next week and couldn't get time off so I had to decline this offer as well. Not 10 minutes later, I was hit with a "I don't think this is going to work out" text. She said we were happy but claimed our schedules don't align and that we won't have time for each other. After a little back and forth with her, I think her belief is that I don't include her in activities with my daughter and that I don't invite her to my house (which is partly true as I go to hers often, mostly because she has her daughter (7f) most nights). I also have a lot of shame and anxiety around the state of my house right now because I still have a lot of my ex's stuff (she was supposed to get it all cleared out this spring but a health issue set that back). My daughter is at the age where doing anything with a parent is cringe and spends most of her time in her room unless we're at the pool. The only other activities we have done in the past few weeks was going to a circus (girlfriend and her kids came along) and went to a movie (girlfriend was invited but unable to go). I don't feel like I'm excluding her from activities, we just haven't done a lot besides the pool, which she is always invited to.

The part I struggle with the most is that we still went to the pool Tuesday night with her kids, she hugged and kissed me upon arrival and before she left and we held hands some while we were there. But the other half of the time, she seemed to be ignoring me. Now in a text this morning, after opening up about my insecurities and worries, she said I didn't give her time to understand and judged her. I'm just at an absolute loss as to how to move forward. The next opportunity we will even have to see each other is Sunday and then she's gone for a week beginning Monday. Do I take a step back and hope she realizes that we had things going well or do I keep pushing and fighting for the relationship?

I'll try to answer any questions that may arise in the comments or with an edit, as I'm sure I've missed some details while typing this out on my phone.