If you're prepared to back right off from the friendship if things don't change, then i'd at least give her the opportunity.
ASK her why she returns your calls at home when she knows you're not there. TELL her you find it hurtful. That you feel like she's avoiding talking to you.
TELL her that you're planning a no-children ladies lunch and invite her to come. Allow her to decline if she simply cannot leave john. This one has to be up to her to miss out on things. You possible could try pointing out that she's stopping her husband and John from forming a special bond by doing things together just the two of them.
Honestly, it sounds like she has chosen to put her son over her relationships
with others. Some people do that, and that's fine. But what's wrong here is that she
is now criticising you
for the lessening friendship, despite it being due to her making it less and less possible. I think it would be good to at least stop this unfair (and rather passive aggressive) criticism. That alone might solve a few things.
I like this idea: invite her to lots and lots of things, but make it clear that they aren't something she can drag a toddler along to, and then it is her
who is declining spending time with you. Make this clear when you speak to/contact her. "Oh, you don't want to come? Aw, that's too bad. We'll miss you. Never mind though, I'm sure you'll want to come along next time." And yes, it is
her not wanting to socialise with you. In her mind, she wants to be with her son more than she wants to socialise with you. Don't be nasty, but find neutral ways to make this very clear.
I also like the bolded above. Stop playing phone tag, because it's silly and clearly she is trying to do something here that's quite immature. I'd stop texting her with your location, since that doesn't seem to work--just say outright, "I'm not at home and won't be for ages, so if you'd like to chat please call my mobile." Don't make it a big scary confrontation, but ask her casually when you next get the chance if there's something wrong with her phone that makes her unable to call home phones. When she says "No", then look puzzled and ask why she keeps calling your home phone when you've told her that you aren't home. Do it in a, "Can you help me work this strange puzzle out?" kind of way so she's working with
you rather than against you.
When your mother mentions her gripes, respond with, "I wonder why she tells this to you? She won't contact me even when I ask her to call me! She won't go out with me no matter what I invite her to! And she's complaining to you instead of talking to me! I just don't know what's wrong. Anyway, bean dip?" Either your mother will stop passing these things on and stop listening to them because she realises they are groundless, or the message will seep through to your friend.
Put the onus on her. She is deciding not to socialise. She is deciding not to call you to talk. But she's doing things in a very circuitous, passive aggressive way and blaming her choices on you. I suspect that either she secretly wants to socialise more but knows her choices make this not very possible so is doing this to make an excuse for herself, or, maybe there's a bit of a nasty streak in her and she enjoys manipulating you. Either way, make it clear that she is deciding these things. Start asking her why she doesn't want to chat or socialise. When she uses excuses like that she called you and you didn't answer (i.e. she's making it your fault now), respond, "No, you called my house when you knew I wouldn't be at home. So why don't you want to chat? I really miss you etc."
She is depriving her husband and child's father of forming a bond with him, quite possibly, yes. But I wouldn't say anything about this, as it ventures into the unwarranted advice that pregnant women and parents get all the time. They're her parenting decisions and it's rude to challenge them. Accept them or walk away, don't try to change the way she brings up her child, even if it doesn't seem like a particularly great way. If she doesn't want to have anyone else watch her son for an hour, that's her choice. But she shouldn't be blaming the results of her choice on the OP. That's unkind and rude.