Going in a totally different direction than other posts here for the last page or two. Or dozen. :)
I want to go back to a couple earlier points - your wife shopping because it makes her happy, and driving all over town every day to keep the children occupied and entertained.
There's a real opportunity here. For whatever reason, through your posts here the day to day life of your family members is coming across as somewhat unfulfilling, like a void that needs to be filled by external things. Not that they hate their life - but that something on a very fundamental level is missing.
Other people are saying drop the blog side hustle, put ALL your time into negotiating credit cards, researching when your foreclosure might happen, tax laws, etc.
As a person who is working to undo 30 years of accumulated clutter in my own house, now that I'm retired - I see that I am making good progress but I cannot just clean and craigslist and donate to thrift shops every minute of my waking life. I can keep up with regular chores, and accomplish one or two other tasks on my infinite to-do list and then I hit a wall and need a break.
I understand why people are saying you can't take a break - this is an emergency. Going back to the hair-on-fire metaphor, you can't be the fireman and decide in the midst of the fire - I'm going to just sit for ten minutes. Because the fire will get worse. I get that. But also - I get that you will need some down time. Even firemen battling raging wildfires take shifts.
What I want to toss out though is that a different sort of break might have more value to your family. Your blogging side hustle is about you getting a break to do something you find fulfilling. But you have a wife who is struggling to find something other than shopping that makes her feel happy. You probably get to talk to other adults in your day to day job, and then the side hustle is something you find intellectually stimulating on top of that. It's so much harder as a stay at home mom, spending all the waking hours solely interacting with toddlers. And you have children who apparently are struggling to find happiness on their own, who need to be entertained by outside activities or things. What if you used your spare time to create family experiences and traditions and memories with your wife and children, instead of coding a website, or retreating to a mancave in the basement to watch a giant tv or play video games?
It could be building an outside temporary fort with the kids (out of items you find, blankets and chairs - not a trip to the hardware store), and having a picnic in it once a week - and having an indoor picnic weekly if it's raining out. It could be a talent (or "no-talent") show once a week, where you take turns singing, or telling a joke, or doing a dance, or performing athletic feats, or telling a story, or doing a puppet show. You could have a weekly "kids pick a meal they like, and we learn together to cook it" night. Find multiple things like this that add value to your family life, and make your time together what brings happiness to your wife and the planning for these things during the day could be the thing that keeps your kids actively engaged in the world, instead of outsiders having to create the entertainment or environment for them.