Breakup advice any input welcome please

Hi my girlfriend and I split up 2 months ago over my doing and how it made her feel. I wasn't cheating btw it was to do wit a previous relationship wit 2 kids involved. I cudnt bring myself to tell them I was wit someone new and she wanted to do things right. The mother of my kids knew I was wit someone but my kids didn't and I was afraid they wud hate me. I have done all the things tha is a no no wen tryin to get ur ex back. Begged pleaded and guilted her but only hurt myself and her more by doin tis but I wasn't thinkin at the time and was worried I'm losing the luv of my life. We went tru all the emotions and hav been tru a lot over the few years together and she didn't want us to hav to hide our relationship anymore from the world. Everyone knew accept the kids. I was wrong about everything and realise that now. Anyway my ex said to me she needs space and all she can offer me is a friendship. Even tho I was wrecking her head for weeks fightin and being frustrated and upset she still did not ignore me and txted me back every time even tho she didn't want to. Wen i realised I hav probably pushed her away now by my actions I decided ok giv her wat she was askin for and let her get space and hopefully be friends in time. So a week past and I txted her asking cud we meet for a coffee and a chat tha I wanted to apologise to her about the way I acted about everything and to see if we cud put it behind us and move on as friends if tha is stil wat she wanted and wen she was ready. She agreed and said she wil meet up soon wen things are easier but we cud txt a little if I want. So I jumped on tis offer. So any way we had a short chat about wat we hav been doin lately and didn't talk about us or anything just chit chat really. I kept it brief and positive. I txted her yesterday for a chit chat again to try break the tension between us. I got no reply at all. So I sent her a little message about how adorable it was the way she don't text me back and made a little joke about it. She txted back straight away sayin sorry she was ament to txt me back but had to rush to work. Now she never ever cudnt txt me in work or even on the way to work (she works nights btw). She said she was asleep all day. Which was 14 hours from my first txt. I took tis as her tryin to be nice to me but still needed space from me. So I texted her sayin maybe I am coming on to strong lately and il back off and she can txt me soon wen she is ready because I don't want to be pushing her into talkin to me if she doesn't want to. I was tryin to giv her the chance to get me to back off abit because I don't realise wen I'm being pushy like tha. I got no reply from the and thought on she is totally done wit me one message in 20 hours is a gud sign she don't wanna talk right now. I woke up this morning to a message sayin To stop sayin stuff like tha and just try keep things normal. If she needed the space she wil tell me. So we exchanged a few messages after tha this morning just possative chit chat. Me tryin to make her laugh and her tellin me I'm a dope ha. I kno tis is a possative sign because we are talkin instead of fightin. I got the feeling she didn't want me anymore last night but today it looks like she does want to talk. Shud I look at this as a positive thing tha we might hav a chance to sort things out? Is this a sign there is a chance to sort this out with her? I don't want to push her but I also don't want to lose her either. I hav been talkin to my kids about me and their mum split up and that we are going to meet new people and move on someday and their mother agreed wit me and kids shud be fine wit everything. Just need to approach it in the right way with the kids. I don't want them upset no matter what.