Four kids and living overseas. Bless your heart. I had two and always went home in the summer. My kids needed and wanted the American experience. It was important to them and I needed to give it to them.
Their first stay away camps were "starter" camps, for 1 week. The next year they attended the 3 week regular version. I also put them in a YMCA day program for a few weeks because they had a water program there.
I also expected them to do summer bridge work so that they wouldn't get behind in school.
Unlike your first grader, my kids didn't have academic issues during our time overseas. Honestly, I think that's what you need to work on. Your daughter needs to mature this summer and to be honest, I think you need to get some help for her in this, rather than spending the money on flights to the US or a trip to Switzerland.
Ask your expat friends (facebook? email lists from expat clubs, etc) if they know of a tutor in your area during the summer who has experience with your daughter's grade level, perhaps someone who has been an elementary teacher prior to coming abroad. Sure, you need some vacation time, but do it in your own country where you can ride the train. A beach or lake would be good - it's a much cheaper change of scenery.
Your daughter needs reading, math, and writing this summer. Let her pick out books she likes - fun stuff. Give her rewards for books she has read (US libraries have reading programs like this.) You list the names of the books so that it's there for her to be proud of. 10 books equals, say, an ice cream cone, at 30 books whatever thing you know she likes a lot that you want to give her. Then for the next 10 and 30 books, the books need to be a little harder and a little thicker books. (Not too hard, by the way, but the next groupings can't be too simple or short.)
Play card games with her. Use a regular deck of playing cards and mix them up, lay them in rows horizontally and vertically, and make a game between you and her turning them over in pairs, looking at them, and turning them back over (start with like 20 cards, making sure that you have put together 10 pairs of cards). Keep turning them over in turn to look for pairs. It tests her memory as to where the cards are. You remember that you've seen the card before, and hope she will remember where she saw it. Make the pair, you keep the cards. Whoever ends up with the most pairs wins.
Find some easy mazes online. Teach her how to go through the mazes with her pencil. Have her make up stories and write them down with her. You can script while she tells. Just write action words and nouns as she tells the short story. Then get her to "help you" fill in the story. When she writes them with you, put her on the computer with very large font and let her type it. Help her edit a little. Help her find clip art and put a picture on her story.
You can also write story lines on construction paper and lay them side-by-side on the floor. That's different than "regular writing" and kind of exciting for the child. You can staple them together when she's done.
There are computer math games that are fun, and teach concepts. What you do want to make sure is that you do INCLUDE math on paper. She'll have to do that in school and you don't want to just let her have math fun on the computer because school won't let her do that.
Spend 2 hours every morning on fun academic work. That earns "x" privilege. For the younger kids, have them do art projects, read them books, work at the same time your daugher does.
It's an important summer, mom. Your daughter will need to step up to the plate for school in second grade. It's her pivotable year because 3rd grade will be HARD. You've got one school year for her to get to where she needs to be.
If you don't have help in the house, please get it. Having someone to support you with the home and children is so important in a foreign country. Of all people, I know there are stressors that you go through that those who haven't experienced it before don't go through, and you need time 'out and about' with other expat ladies to help you find some joy in where you call your temporary home.
As far as your parents are concerned, could they come visit you? As long as you continue having a schedule in your home for the children, it should help your parents. They can retreat into their room when they are a little overwhelmed. If they do come, make sure to have a babysitter watch the kids so that you can take them around and give them plenty of attention that you couldn't give them if you had 4 kids in tow.
I wish you all the best this summer. (Hopefully next summer a real vacation will work out better...)