I was in the same situation but I was the father... I prefer not comment more on this...
My advice? Go to America and come back time to time to see your children that probably are living well integrated here.
As to your job: you probably got that based on your husbands nationality/family reunification?
I‘d imagine your employer will need to apply for a permit if you are no longer here on family reunification.
The courts - and even though you are not married, the courts, or some other authority, may/should be involved for formalise the agreements between you and tha father of your children, about the children and the money - can (and do!) even prohibit a parent from moving the children far enough away that the access to the other parent becomes difficult.
You can, indeed, take the children further away from the domicile of their father, and even outside of Switzerland, but only if you can demonstrate that this is in the children's best interests, and if you have a written agreement with their father that he allows this and specifying how the children will still get to see him.
You might also find some of the discussion in these related threads helpful:
https://www.englishforum.ch/permits-…h-breakup.html
https://www.englishforum.ch/family-m…d-custody.html
https://www.englishforum.ch/family-m…dy-matter.html
If you have an independent permit, then you can continue to live and work in Switzerland, for as long as the permit lasts. If you are properly employed, able to support yourself without needing to claim help from Social Security and if your contract is ongoing, there is a high chance that your permit will be renewed. Be aware, though, that the language requirements are a stricter criterion now than formerly, in order to get a renewal.
If your permit was granted in the course of family reunification , based on your having been a couple, then, when the grounds fall away (you and he no longer together) so, too, will your permit end.
There have, however, been cases where an exception is made for a foreign parent. The decision is individual from case to case, and will depend on such factors as the nature and intensity of your relationship with the children the children's ages your proof of your integration (measured by such factors as, for example, your command of the local language, your working in an ongoing contract, your participation in life outside of your home in your own clubs, societies, activities to do with the children such that you interact with other parents, your own and your children's doctors, your relationship to the school staff and your neighbours). How many of these kinds of factors be regarded, and how much considered irrelevant, is largely at the discretion of the official deciding about your case. The onus is on you to provide all the paperwork they ask for, and also to show your integration as it is and your willingness to improve it (if still necessary beyond the level you already have now). In general, the more fully and plausibly you can demonstrate that you're settled here and feel that you'd like to stay, and can prove that you won't become a financial burden on the state, and that your children need you, the higher your chances of getting a renewal.
Maintenance/alimony for the former partner
In general, it is considered normal for each adult to work to support him- or herself. The former notion that one former partner will necessarily support the other is now no longer the norm.
Some exceptions can be made if one partner has always or mostly stayed at home to care for the children, and the other has earned enough for the whole family, but please note that even for married couples divorcing, such personal maintenance payments are usually limited, for example for two or three years until the formerly-stay-at-home parent can complete an education to become self-supporting, or until the ages of the children (and how many hours they’re out of the house at school or child-care) reasonably allow for this second parent to return to employment.
Even so, please not that for unmarried couples this support of an ex-partner is by no means standard. From this Swiss government site about living together as an unmarried couple: https://www.ch.ch/en/family-and-part…n-consequences
If you separate, you are not entitled to maintenance payments, even if you have reduced or given up gainful employment during your partnership in order to look after the joint children or the household. Some unmarried couples who split up do, indeed, decide that the higher earner will support the other, at least for a while, particularly if they can handle the matter relatively peacably, and if both parents would prefer that one (or both) work only part-time so they can take care of the children.
Child support money
Child support payments are, however, a separate matter. For this, both parents are seen as responsible for the costs of the upkeep of their joint children. If there is a great discrepancy in the earning potential of either parent, then an agreement can be drawn up that the higher earner will contribute more.
Where parents have shared parental authority, then they are, in any case, supposed to discuss and agree upon large costs, such as major dentistry, grand holidays, the purchase of large items such as a new pc or special sports gear, etc.
AFAIA a couple moves in together, that's it. You don't get to have a family reunification because there's no family to be reunited without marriage certificate or equivalent.
Although I haven’t investigated this further or read it in depth, at first glance there does seem to be provision for permits for “Konkubinatspaare” (unmarried couples) on this site, as long as the relationship can be shown to be long-term, in which case the unit is, indeed, considered as a “family”, at least in some aspects… such as the permit.
https://www.zh.ch/de/migration-integ…ml#-1522218545
OP, is your permit connected to your Swiss father-of-your-children, or not? As I wrote above, I think this will make all the difference for you.
Basically the working partner with the permit has to agree to support the partner and prove that they have the means to do so just the same as for a family reunification permit. (For 5 years initially I believe)
The requirements are quite stringent and the authorities do generally expect the couple to have plans to marry at some point.
So the default (assuming that exception is not granted per above) outcome in case of divorce with a Swiss parent is that the foreigner on family reunification permit is permanently separated from their children? Since they are not allowed to bring the children out of Switzerland, but also they themselves are not allowed to stay in Switzerland?
This seems absolutely, positively, insane.
In some cases, the foreign parent making the application to be allowed to continue to stay, has been deemed to have fathered or borne the child only to try to manipulate the immigration authorities into granting a permit. They don't like that.
As I understand it, it is precisely to try to prevent children being thrust into such confusing circumstances that the law has been amended to allow for a case-by-case assessment. As long as the foreign parent can demonstrate that he or she is not likely to need to depend on Swiss Social Security, and show evidence of integration, there's now a much higher chance of their being allowed to stay.