Need advice. Are these red flags that I'm seeing? Should I abandon any hopes of a future relationship with this woman?

Ok, so I suppose i should provide a little context/background information to this question.

I'm not even 100% officially divorced (should be finalized within the month I believe). My (40M) STBXW (40F) and I separated in July after discovering her affair with a good friend of mine. I swore off women and dating forever, and honestly, still am very unsure if I want to venture into a relationship again. Of course as fate would have it, I was approached on behalf of a friend of a soon to be divorced woman (30) when I was out with friends one evening in October. We exchanged numbers and texted for a few weeks getting to know one another. We went on a few dates, and seemed to get along nicely. I made it clear to her from the beginning I wasn't looking for anything serious or even sure if I was 100% ready for a relationship and she was fine with that and wanted to take it slow.

After a while, I was starting to get the impression she wanted to get more serious (meet her family, spend the night, etc.). I wasn't ready for that and communicated it with her. She seemed to understand. I then started to struggle a bit with the idea of being in a relationship this soon. I have two young boys, and I have been having a hard enough time making sure I'm doing all I can for them during this difficult transition. So, I told her I wanted to end things for now. I didn't expect her to stick around and wait (even though she said she would), and I had no intentions of dating anyone else. I just wanted to take time for myself and my children to figure things out and I didn't feel it was fair to string her along if she and I were not on the same page with regards to what we wanted right now.

She took it hard for a while, but was never crazy about her reactions, just very sad. We haven't really talked a whole lot in the last month and a half, save for the occasional text here and there.

Now here is where I have questions. Apparently, about two weeks ago, she reached out to my STBXW and asks if she would be willing to meet her so she could get a better idea of who she was (my STBXW did not like it when she found out who I was dating). Apparently she wanted to put out an olive branch so to speak so she could try to establish some trust (which is all well and good had we still been dating, but we aren't right now).

The second issue came up yesterday. She reached out to me for the first time in weeks, and we exchanged a few texts. I told her about some health issues I'm having (back problems) and my dad is also having (we think a ruptured disc). I mentioned how my mom was very stressed dealing with it, and we pretty much left it at that.

My mom told me last night that she reached out to her and said she was sorry to hear about my dad and if there was anything she needed, to let her know. Mind you, my parents and she have never met. They knew about her, but never met her, nor had the spoken to her before.

Part of me thinks that was nice of her to reach out, but part of me thinks it's...I don't know...strange?

You have to remember, my STBXW was my high school sweet heart. I never dated past her, and I have no idea about what is and what isn't red flag behavior, lol.

Thoughts?

TL;DR;: Should I consider a future relationship with this woman that reaches out to people in my life when we're NOT actively dating?