We generally advise against international travels solely for the purposes of polishing your CV. Mobility should always rank secondary to research output, ideally it should be integrated into a research project in order to generate added value.
The SNSF excellence fellowships enable you to spend time at a foreign university and work on parts of your doctoral thesis abroad.
Moving to a new location with family and partner might be a little difficult, despite the fact that the SNSF awards partner and child allowances. Attending conferences is a little easer compared to moving overseas. The SAGW and the University of St.Gallen offer financial support. You might want to adopt a strategic approach to planning these opportunities: check the list of participants in advance and think about who you would like to connect with. Do not skip the informal part of the programme, especially if you know you are not a born strategic networker.
International networking can also happen at your home university. Maybe there is an opportunity at your institute to organise a conference and get in touch with well-known researchers.