With regard to custody, Swiss law distinguishes between "parental authority" and "residence". Parental authority includes taking the important decisions about a child such as schooling, health matters, travel, special training in sports. Residence means where the child lives.
While the parents are married, they automatically have shared parental authority . It is now the norm to uphold shared parental authority beyond divorce. The idea that one parent "wins" full custody, to the exclusion of the other parent, is considered out-dated.
The parent with whom the child resides takes small decisions without having to consult the other parent, such as bed-time, when to do homework, when to brush teeth, what to eat.
Even residence can be shared , with the children living with one of the parents for half the time and with the other parent the other half of the time. This is not yet the norm, but can be awarded in some cases, especially if both parents are actively interested in taking care of the children.
In all cases, the guiding principle for the judge's decision is "the best interests of the children", and it is generally considered to be in their best interests to have free access to each parent. Of course, there are bitter exceptions, of which there are some threads on this forum, in which one parent, and sometimes even the children themselves, end up fighting just to be allowed proper parent-child time. The child, though, has a right to be able maintain a relationship, easily, with both parents.
Given all this, it is often not possible for one parent to take the children out of Switzerland, or at least not without the permission of the other parent. This even applies to moving, within Switzerland, to the other side of the country.
The reasoning is that removing the child so would inhibit the child's rightful access to both parents, and that the parent with whom the child does not reside (if no shared residence) would, by the child living far away, be inhibited in his/her exercising parental authority.
As to lawyer's fees: the more you and your husband can agree on the terms of your divorce, both with regard to un-hooking your finances from each other, and in terms of the care of the children, the less there will be to fight about, and the lower the lawyer's fees will be. Then you can spend the money you've saved on lawyer's fees, on the children.
In this thread, https://www.englishforum.ch/housing-...t-anymore.html , I posted some suggestions to keep the lawyer's fees low.
General info:
https://www.ch.ch/en/divorce/
https://www.ch.ch/en/divorce-parental-authority
You also need to check your residency/permit situation: https://www.ch.ch/en/right-to-reside...th-or-divorce/
This is a condensed version (in German) of the main points about Eheschutz.
https://www.ehescheidung.ch/trennung...atte/eheschutz
Here (in German) is an article in the Beobachter, a reputable magazine reporting on social issues.
https://www.beobachter.ch/familie/tr...ind-auswandern
It links to two Swiss Supreme Court judgments, one in which the mother was not permitted to take her minor children away from Switzerland and their father (though she could have left alone) and the other in which she was given permission to take the children. Both judgments emphasise that to stay or to go must be decided according to what would be in the best interests for the child.