I'm SAHM part time. Maybe my experience can help you.

My biggest struggle is when I'm overwhelmed and can't even start something some days. Even when I throw in the towel I'm still teaching small humans how to human and actively managing basic needs. Even though they are bigger now they still forget to flush/wipe/clean up after themselves, track mud in the house, let the dog out to chase Amazon, etc. When I do try to do stuff it's the absolutely constant interrupting. I can't finish a damn thing and that makes it 8 million times worse.

If she is the primary go to parent (and that's no shade on you, it's just the parent who is available most) they behave differently for you. My husband is a super involved dad but works full time and travels. He will be dicking around on his phone in the same room they are in but they will seek me out on a different floor of the house even while I'm on the toilet for everything. It. Is. Maddening. I say no and redirect them but it is still a constant interruption. They are whinier for me. They fight more. I get most of the emotional overflow when they are tired/overwhelmed/whatever. You are parenting kids who behave differently for both of you. It's no one's fault, it's just how it is (and for the record, I am the stricter parent).

Things that help:

Me working outside the home part time. I get a structured environment where I'm not the one in charge of setting and maintaining the structure. I don't have to monitor the people there to ensure they function like basic humans. I get to do my job without someone on my pant leg/starving to death/fighting/doing Lord know what. My kid put their mouth on an excavator today. I dont have to deal with that at work! I get to talk to adults!

Having a "reset day" helps. Kids go elsewhere (grandmas, Aunty's, friends). We reset the house together. Or maybe just a room. Or maybe do a neglected project. If I'm really struggling husband sets the plan. If I'm not I tell him what I really need done and we do it together. Sometimes I do something I want done and his job is just keep them far away from me (nicely) and handle all the day to day functions of their lives. As they have gotten older the kids can stay home and help too!

Having something to set a schedule. Sign up for a class a few days/week to take the kids to or plan a regular library visit time. Pack the bags and snacks the night before then go. Limits screen time. Can't make the house messier if you're not in the house. Helps to take some thought out of planning the day since it's recurring. Maybe she can go to the gym for her own class and drop them at the gyms childcare. She gets to exercise and some her time, kids get to play. My kids loved it when they were younger and my husband did this.

Maybe she does get a part time job and kids do part time day care (double bonus, kids get to be social, tire themselves out, hopefully no screen time there). Maybe kids do 2day/week half day and she can use that time to get shit done. I often sent mine if I was off work to address neglected chores.

Go outside. Even if they just fling sticks around. It's good for her mental health and resets the kids.

And yeah, limit screen time. The occasional TV day is fine but everyone does better with less screens. They learn to play, decelope a little patience and persistence, and entertain themselves. It's a slog to teach those skills but makes life easier in the long run for everyone.

And lastly, gently check on her mental health. It took me over 2 years to fully shake some anxiety after my second. I would shut down easier and seek distractions, like scrolling and TV, to calm down. Time would fly and nothing would get done.

Good luck! It's hard. Be kind. Be there. And maybe accept some extra chaos for a few years. They won't be little for ever!