You think you have problems.
My old mates surname was Pratt.
His life was a nightmare!
His nickname was 'Aright.'

I try to avoid using horrific chemicals whenever I can, so for weeds, I pull them out.

This works much better with agriculture vinegar or a vinegar over 20% . Standard white vinegar is usually 5%.

weed
 

pursalene. Its everwhere,Its everywhere

Yup. In the back of our CYV we use white vinegar epsom salt dish detergent mix but I don’t know if it really kills the weed. Slowly pulling out of the ground works for me. Surprising how extensive the root can be. OP’s picture looks like pretty mature weed. We live in a CYV with a dog so don’t use poison in the back. In the front we sparingly use Roundup unfortunately (when I’m not just yanking them out of the ground)

Simple, keep your expansion strips cleaned out by jet hosing them to prevent weeds from growing in them. That lacey type of weed is fairly easy to pull out. If you have rock beds clean them out, use a good weed killer if you have trouble pulling weeds. Use Preen on rock beds to prevent them. I use a weed torch to zap the few that pop up.

weed killer
 

Ortho ground clear.
buy at Home Depot.
a little pricey but does the job
can be bought 2 ways

spray bottle already mixed under $9.00

1 quart concentrate mix with 6 oz of water $24.00 If I remember right of close to that price

...

Spray it as soon as you see it. It is a prolific seed producer and can spread fast. Look closely at your lawn it is probably there and that is where the seeds are coming from. .

Use a post-emergent herbicide, but VERIFY IT WILL NOT KILL THE TYPE OF GRASS AROUND THE WEED aka “Floratam” St Augustine. However, this crab grass here (planted as "lawns") is very sensitive to "safe to use" stuff, if applied too concentrated.

Maybe this would work... 3 Way Max Turf and Ornamental Broadleaf Herbicide
domyown {dot} com/way-max-turf-and-ornamental-broadleaf-herbicide-p-9853.html

For the broad spectrum, kill it all, approach... There are 2 types of weed killer actions.
Roundup equivalents work for a short time, a day or so, because their active ingredient is broken down by sunlight. It absorbs into the week and fills to the root. This is what you use around other vegetation.
Veg killer type are long acting. Kills now and remains in the soil active for months. This is what you use in driveway cracks.

Never simply pull it out. Pieces of root break off and remain alive in the soil and will regrow rapidly. That become a full time, never ending job. Weed killer first, wait, then pull the dead remains.

A good trick when spraying is to surround the weed with a cardboard "wall" to prevent over spray.

I’m sorry to hear about your wife. I hope whatever treatment she is receiving is effective.

It’s better to use Roundup than a vinegar solution in the garden, although both will kill weeds. Roundup becomes inert when it hits soil and doesn’t affect anything grown there afterward. Vinegar will make the soil more acid until it dissipates and can kill anything planted until it does.

Instead of spraying Roundup, put some in a container and paint it on with a paint brush. It won't spread to other plants.

Green Goblin. Buy it at Ace.

Very common weed. Just spray to get rid of it.

I used Ortho Weedclear which you hook up your hose and spray your whole lawn. Worked great. Took care of this weed as well as all the chamber bitter that is very hard to kill. Didn’t hurt my lawn