@Gwenhwyfar
"On the weekend she spends time with her husband and baby and socialising as a family with other couples/families. That's perfectly understandable."
If she can socialise with other couples/families, why can't she socialise with OP?
I know some people only want friends who are couples and families. I wouldn't bother with those people.
Because as people have already said it's more effort. If you go out as a group you don't have to stay 100% focused on the conversation at all times, one of you drives while the other entertains the DC, your DP or family are there to help share moments of childcare at the venue, your DC can play with the other couples DC. It all adds up to the situation feeling easier and it's time spent with your closest people, your family. Even if it's friends, you're still socialising as a family with your DP and DC.
With a one to one friend meet either you've to negotiate child free time with your DP, so not only do you have to fit in your friend, but you're almost certainly going to be lumbered with a sole childcare time afterwards when your DP decides he wants me-time too. If he's a bit of a git, as so many ordinary, on the surface apparently "reasonable" men are when they don't get their own way, he might take twice as much me-time as you have, he might agree to have DC but grumble about it all weekend and expect a gold medal too, or claim he's now too tired to help with house chores. All of which adds to the mental and physical effort of fitting in that visit with your friend.
Or you've to get yourself and DC to the venue, stay focused on your friend the whole time, whilst also accommodating your DC need for attention and keeping an eye on them when they're not demanding your attention, then gets yourselves home by yourself again. It can be extremely tiring. Then you get home and there's all the usual stuff to do, which hasn't magically done itself whilst you were out.
Could also be that her DP wants to socialise as a family with these other people regardless and is being inflexible about that. So meeting up with a friend would end up being on top of that, for her.
Then there's her DP who you get on fine with OP. I get on fine with lots of people too, including ones I don't like or aren't that bothered about or find slightly annoying, especially if they happen to be my DP friend. I would never ever tell them, would remain polite and friendly, but you bet your life I'd put my foot down about having them in my house every week or having to meet up to socialise with them once a month. My downtime is precious to me. So the option of you socialising with your friend as a family group, which you're willing to do, might not actually be an option.
I imagine your friend has been quite blunt about this boundary OP because she's had to be. You're a confident person and there's nothing wrong with that, but inviting her out on weekends is pushing her boundaries when she's already told you no in advance. You're not taking her decision well as this thread shows. I expect she knew this is how it would be and that's why she felt the need to be so outspoken from the beginning, so there could be no misunderstanding and she wouldn't feel under pressure from you. How many times do we see it on here? If someone is being pushy and won't take a hint, communicate your boundary in the simplest terms and then stick to it. If she came here that's what she'd have been told and it's what she's done. Perhaps it needs to be a concrete boundary for her because if she gave you one weekend meet up during this 7 weeks, which to her, depending on her situation, could be majorly putting herself out, you'd still not be happy and would just push for another a few weeks later. Perhaps the only way she can avoid feeling pressured is to make it a blanket no, never.
With the texts effectively calling you out for disengaging, it's difficult. On the one hand she could be trying to show you she's not trying to fade you out, which is nice, I guess. On the other hand it's taking the piss somewhat to make it clear to someone they're not your priority, then get sad and call them on it when they disengage!