Motherhood is a 24/7 job. See it as, when at work, you do find the time to meet your work colleagues during lunch breaks for coffeee to discuss things about work which ends up clearing your mind so you can cope through the rest of the weak and bounce off ideas..
You can do that even when u don’t have time to answer your dads call about visiting him this weekend because unfortunately when mentally drained things that you usually enjoyed can become a burden if it doesn’t help you deconstruct what’s consuming your day.
However it does usually mean that the balance isn’t there, the person is overworked...
Ur friends aren’t behaving in a way healthy to them or their lives but they probably know that and wish they could. Motherhood to small kids is a mental struggle.
Don’t compare yourself to their meet ups with mum friends.
First of all the kids playing together usually is the highlight of why they are meeting and because they need to share the load of 24/7 attention and discuss the challenges they face and maybe have a small healthy competition and little boast about their kids bedtime to give themselves a pat on the back for taking that extra step forward.
It’s not mentally fulfilling. For someone with a very exciting career these conversations will probably be far from socially fulfilling.
I thought I was doing a good thing inviting my child free friend to a group of mum get together where the rest of us had our kids at soft play and we used to all be close. She seemed lonely and irritated, and sat by herself contemplating and seemed drained by the occasion. Not fulfilled..
The rest of us felt “relieved” that our kids got to release the energy and be mentally stimulated without us having to use our small energy reserves.
Truth is, most occasions, nothing about motherhood is about the mother and her needs.. even socializing is about the kids.
Especially in the first few years of their lives until they’re in school or so.
It’s really not personal to u but I understand the feeling of rejection of there is no reciprocation.
For me, I wait for the minute my son gives me a break so I can sleep or finish the laundry pile. I’m quite behind and never feel like I have time where I’m bored with nothing on my to do list.
I schedule time with my child free friends because it’s the healthy thing to do. But I feel depleted after,
Because it’s usuallt about me trying to minimize the fact that my attention is on my bored toddler because I feel guilty and boring to do that around her. I try to have conversations with her about things not to do with kids because it gets me back in touch with myself as an individual but it’s totally motivating to see myself in this way but after the meeting is over and practicality of the situation hits and Then friends asks me for updates and what have I done so far to achieve my dreams.. and what I’ve been up to the last two weeks... I feel a great sense of shame that I have failed myself. But because me and myself are not on my mind during any of the days I’m not meeting her because simply I’m fully consumed by responsibilities.
Motherhood has become such a huge task because before everyone shared it and the support was immense from society and relatives but now it’s just the parents..
So it’s quite intense more than biology was designed for.
Your instincts are telling u the right things about motherhood.. but reality is that nowadays motherhood has become just more than that..
It’s worth it and deeply fulfilling but requires huge compromises on many levels that leave you feeling unaccomplished..
I wouldn’t like to sit there with my child free friend listening about all her projects which she submitted which I’m happy for her about and then shamefully answering her question of “what have you done all week”, and I saw, wiper bums, made food, ran after toddler in park... slept when I could.. stayed up all night for teething.
While she looks at me blankly waiting for something she can acknowledge as an accomplishment 
and me knowing how boring it all sounds.
The beauty of motherhood is sentimental. Something you feel when you are doing all this. The progresss is eternally slow. And milestones you feel are huge to u are small in the grand scheme of things.
But when I’m with mum friends I see great empathy on their face asking me whether my toddler managed to sleep well last night.. and I can feel accomplished by telling them he ate his broccoli for the first time.
Motherhood is beautiful.. really is... but even my DH is very bored when I’m telling him how my day went 😂😂 and I’m envious when he tells me about all the meetings he had and all the awards he won. If it’s not for my mum friends I would feel like my life is at a standstill.. which is often how it feels like to many new mums and mums of very young ones.
But that’s not to say friendship isn’t possible.. it is.
1- you could work out whether you are interested in her new life? By meeting her in playgrounds while she is playing with her child or have a group catch up with friends some are child free and some not , in a child friendly place ? Coffeee shops are incredibly boring for kids.
2- schedule some nice me time for you and the mum and let it be at her own time. Let her know you think she has been working really hard with her kids and it’s consuming her and so you want to encourage her to some me time.. so you can ask her when her DH takes the child on the weekend and you two go to a hair salon where she can finally get her haircut!? Or she can bring her child and you take turns in looking after him/her while you chat over pedicure?
Unfortunately you need to just accept mothers put their socializing needs at the very bottom and can only work out this part when they have their kids tended to. It’s not a choice. So planning events around that will be deeply appreciated by them until that phase is over.