As a single parent of 2 (one pre-schooler) and someone who does find it hard to let go of things in general and whose home is often horribly cluttered and messy, and sometimes dirtier than I would like, I have a massive amount of empathy for your friend. Really like what @sunglassesonthetable has said. My advice FWIW (and obviously I am only speaking from my experience, and suggesting a place to start, rather than where things might/should end up)…
The house is likely to be a symptom of where she is right now emotionally/mentally
It may, in general, be best to treat causes not symptoms. But in this case you don’t know exactly what the cause is - she might not even know what it is. What is clear is that there a massive amount of overwhelm going on.
It’s important for her to know that you understand. She is not going to accept practical help if she feels judged or if she thinks someone else is going to impose their idea of what needs to be kept or chucked on her. The house indicates she’s feeling out of control - taking more control away from her won’t help.
So the very first thing you need to do if you want to help is spend some of your coffee sessions talking with her and letting her know that you see all the amazing things she is doing so well, and that you really empathise with how hard and relentless her life might often feel. If you focus on what she is doing right she may feel able to open up about where she is struggling. If she does then you’ve got an ‘in’ to say ‘well of course but at least that’s stuff we can tackle - id love to help’.
if she is genuinely able to make three young children feel happy and secure while spending most of her life in a small and messy house, trying to earn money and surrounded by an ever increasing to do list which she can’t deal with then she actually really truly is doing pretty well - you can’t teach the ability to give love, but you can help people with practical stuff, and it is ever so ever so easy to become so overwhelmed as a single parent under pressure that you don’t even have the bandwidth to be as kind and nurturing as you’d want.
If she broke up with her husband when she was pregnant then she has just gone through 0-3 by herself in this situation. 0-3 is a massively intensive ‘stuff’ phase. Dealing with that is a bloody nightmare and you can quickly go from being on top of things to having mountains of things to get rid of/sort out. It’s horrible.
Please also remember that poverty and money worries often do not look like having NO stuff. They can very often look like having masses of stuff, not all working, not all perfect nick. Worrying about money makes it very hard to get rid of things - you need stuff ‘just in case’ as you can’t go and buy it ‘just in time’.
If you really want to help I think you have to see this as something that you’re prepared to view as a medium/long term project, not a short term fix. It may be that at some stage along the way Amy can suddenly feel the fog lifting and is able to seize the moment and move quicker. But to start off, you’re probably going to need to put in some time, empathy and listening on and around her life in general and before you open a black bag or wash a tea cup.
Be honest about wanting to help, but make sure you don’t frame it as “this isn’t acceptable, SS should be involved etc”. What she needs to hear is “I love you and the girls, you’re doing so wonderfully, you are such a great mum, I’m so sorry you’re doing this all by yourself, it must be so hard to do all this by yourself. But it’s not ok that you don’t have a relaxing space to sit in during the evening, you need to be able
to give back to yourself so you have even more energy for the children, and so you can enjoy the brief time they are at their dad’s”.
Please understand that although she might be bright and breezy when she sees you, her daily life internally might be very different. Sometimes things just get so hugely difficult and overwhelming that it’s hard to know where to start. And when you’re emotionally and physically exhausted you’re starting from a very low point. I have had many, many nights where the kids are in bed and I’ve looked at my house and just cried or watched tv or run the laundry because getting started is really difficult. And ignoring, or doing a tiny task which operates by itself is way easier than starting to pull a thread on a bigger task and watching everything unravel around you.
That might be counterintuitive, but that is what I have found. The single one thing that has helped me tackle things is having support in feeling competent. When I feel incompetent I spend energy beating myself up and feeling hopeless. When I feel competent I remember that I CAN do things and I CAN make it better.
I would also suggest that there are probably way bigger issues upstairs in terms of clothes and toys etc etc. one way to help might be to deal with an issue you can’t see on your visits but which must be present which is that of outgrown baby clothes/toys. Perhaps say you’ve been clearing out your kids stuff to take to a charity which provides clothes to families in need - could you and she go through her kids stuff over a few weeks, or one of her ‘free’ weekends, and then you’ll take everything with your stuff to give away? How about suggesting you both put the trampoline up when the weather starts to get nicer and using that as a chance to clear through what’s not being used in the garden.
it’s hard to keep things you use nice when you’re also surrounded by things you no longer need but can’t tackle getting rid of. Baby clothes is probably a great place to start (this worked really well for me).
Have written an essay (so sorry) but I guess I’m trying to say that you’re right about the logjam and when things get that way even the simple stuff becomes overwhelming. It’s very likely she is depressed and exhausted, she just doesn’t show that to you. Try to let her know that you see the struggle - even though she has such an amazing game face and is doing so many things brilliantly. Be there for her. In the long run you’re more likely to be a good friend to her that way, and be able to help, than by making her feel judged, ashamed and small.
Please don’t tell her what she does/doesn’t need, sometimes letting go of things can take a little time. Let kindness be your guide…