Are the children resident in Switzerland at the moment?
Although the original order came from the Court of Session, because the children are now habitually resident in England, this would in all likelihood have to be dealt with by an English court. However, the answer to your question is that an application for joint residency would be competent depending on the split of the care of the children. Whether it is granted would depend on the circumstances justifying joint care of the children and in particular how often each parent will have care. Child support is paid to the parent with care so a joint arrangement would be better from your point of view as you would not be paying child support when the children are away, although I presume the issue of who is paying the fees might be relevant.