How on earth can you be a single mother, have 4 kids, be expecting another and have a job like being a teacher? Its shocking how the gynocentrism in the west supports women to not do the jobs they are paid to do.

Only a couple of generations ago women quit teaching jobs when they got married as a teaching job would clash with their wifely duties. My mother was a generation later and quit when she planned to get pregnant. Now they can somehow be a mother of small kids and a teacher. Their job is kept for them at the expense of their students by hiring supply teachers or short term contract cover. They then dump their tiny children on state funded nurseries and go back to work complaining of "baby brain" while anyone who criticises them for not being on the ball is sexist and misogynist.

What bit of her is left for her kids in a life like this, never mind the father of the children or of course the stand in beta who is in all but technicality a cuck raising another man's seed?

Future historians will put adverts like this in text books to show how western society failed. The one thing this woman has not done to ruin western society is fail to reproduce. That much at least she is to be praised for but all her reproduction has been with someone else picking up the load.

I normally like to autistically cold approach them after just 1 or 2 of encounters

1) if it's anything past the first time you see them, it's no longer a cold approach.

2) I always got better results with what PUAs called a warm approach, which was don't bother her unless she shows interest first. A true cold approach is disruptive and intrusive, and thus more difficult to get what you want. Cold approaches are great for just practice and to build outcome independence, but if you are too invested in outcome (sex), you're going to be disappointed.

3) you shouldn't "autistically" approach anyone, cold or otherwise. Fucking be normal. Have a conversation. Learn to talk to anyone and everyone and be relaxed.

Just wanted your guys thoughts on letting a woman monkey branch to you I guess,

I've never knowingly let that happen. I don't advise inviting complications into your life.

1) bad character. If she does it with you, she'll do it to you. If it's just a one-time encounter, then who cares, but then...

2) jealous men can be very dangerous. I don't care how badass anyone fancies himself, but inviting that kind of trouble into your life is stupid. There are plenty of women who aren't taken. I advise finding some of those.

How df do I tell?

Escalate until they stop you. Escalate until you either get sex or get rejected and know to stop wasting time and energy on her, and move on to the next one.