Hey guys! - and ladies if there are any

.
I've got a slight problem in which I would like some feedback on.
About 1,5 month ago my LTR girlfriend broke up with me, due to the fact that I did not seem ready to be in an actual LTR - according to her. It involved my ability to be responsible in a home which included a woman in it. Im soon to be 25 and I'm still very '
low-amount-of-fucks-are-given' to cleaning, cooking and etc.. I am a very spontaneous kind of guy and I do things
my way.
She, on the other hand, is very much into the routine thing when it comes to the things mentioned above.
The problem here is that this girl is my first LTR and I have developed deep feelings for her, and she says that she has done the same to me. But she thought it a too big of a struggle to change '
my way'.
My response to her was she didn't have to worry about it, and that it would come with time, but it did not help.
Last week, however, we agreed to meet. We wanted to take a walk, but when we arrived to the place in my car, it started to rain heavily, so we stayed in my car talking for 4-5 hours, past midnight. She told me that she had noticed that I had starting to communicate with other girls, and go clubbing but
in addition she told me that she
might be interested in being in a relationship with me again, but she was not sure. She wanted to restart it
slowly - starting as friends.
I said that I was open to the idea, but I would not wait around forever. I still have feelings for this girl, and in the future I could easily see her as the mother of my children.
Well we have texted every day since that talk in my car. She is always the one who initiates contact, which is a positive IOI, imo. But
the issue is that every time I try being flirtatious with her or sweet towards her, she doesn't give anything back. Apparently - or weirdly - she is very strict on this "start out as friends" even though she tells me that she has feelings for me. And I've tried three times now, to set up a casual date - first eating out (rejected), then running together (rejected) then for a late walk (rejected). Im getting extremely confused here. She tells me that she wants me back (
maybe?) but doesn't really show it.
ON THE OTHER HAND: Once or twice a week she goes to a fitness course with a male friend of mine and hers, who has got a girlfriend for years, and even lives with his girlfriend. I don't mind this, because I trust him due to the fact that I am very close to him and his girlfriend. I frequently visit them in their apartment and do casually play online games with him as well.
My ex keeps inviting me to go to with her and our friend to this fitness course. And I don't understand why this is the only place she actually wants to hang out with me - especially with our friend there, so its gonna be us three.
I find this very weird, that she rejects all of my 1 on 1 dates for the sake of this.
What is your perspective on this? What would you have done in my situation?
Lets exclude the solution "Forget her, and find something else". I wanna learn from this situation and turn the tables.
So how can I turn the tables in this situation? Whats your input?
TLDR: LTR Ex breaks up with me as I'm not ready to move in with her, a month later she tells me she wants to get back together, but very slowly as friends. Only wants to hang out with me if it includes a specific fitness course and good male friend of ours who's in a serious LTR himself.
Thanks in advance.