My husband (also an only child) and have I spent the better part of 15 years (and counting) trying to juggle eldercare responsibilities across the pond.
If I could turn back the clock, knowing now what I didn't know then, I would not have moved to Switzerland. Juggling is always a catch-up game; all that effort and everyone, on both sides, still feels let down.
My 5Rp, with the benefit of hindsight: If you make the move, have a back-up plan for one of you to return to the US for a prolonged stay(s) if needed. Consider what that means to permits (and consequences should naturalisation be a goal), child care here, effect on career, sourcing difficult to find services in Switzerland to take up the slack when one of you is gone. I wish we could have done that - but we seemed to always be in reactive mode.
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Balancing our responsibilities on both sides of the pond has been exhausting, stressful, horrifically expensive... and it has meant that we have been unable to take advantage of our time here. We live here, but our lives, by default, had to be there. For the worst of the time, when we were in a critical situation with 3 of the 4 parents simultaneously, every free moment had to be spent in the US.
As you can imagine, traveling to the US every couple weeks for years on end takes quite a bite out of one's savings. But the not-so-small fortune spent pales in comparison to the emotional toll.
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How did we do it?
You need local eyes on the situation.
Organise as many resources as you can in your parent's hometown. Interview agencies, set up contingencies, try to build a network, family friends as well as professionals, who can be first responders in a crisis. Remember, at best you can be there in 24 hours - but more often than not it will be 48.
Try to encourage the parents to hire services, now, that you would normally provide - errands, yard work, handyman stuff. If they cannot afford to do so - or simply do not want to spend the money - offer to pay for it yourself, an investment in peace of mind. Get to know everyone who provides services to your parents personally, and keep in touch with those people.
If your parents are church people, speak with the church outreach staff. Ask what help the church can provide. Many churches offer a variety of senior services.
Keep on your parents' neighbours' good side. (Swiss chocolate helps.) If a neighbour is willing to simply keep an eye out and let you know if something doesn't seem right, that is a godsend. We were blessed with lovely neighbours - one stopped on his way to work to bring the paper from the end of the driveway to the door (a chance to quickly see if the ILs were OK each day), another often popped by for coffee, a third just 'happened' to meet FIL on his walks around the neighbourhood. The advantages of living in a small town in the cornfields of Hoosierland.
Be cognisant of your parent's pride; no one wants to feel beholden, especially those of our parent's generation. Try to keep the stress the situation puts on you away from your folks as best you can. Tough to do, I know - but in the long run it will help your folks accept the help they - and you - need if they do not feel like they are a burden.
Collect information about available options should your parents no longer be able to live in their home. You need this information in your back pocket - because the last thing you need in a crisis is to be scrambling around when you need an immediate solution.
Obviously the best solution is for parents to do this themselves, make their own choices an decisions - but sometimes this is a step - or even a conversation - that is too difficult to have. So you need to do some of this 'in the background'.
Visit all area assisted living, nursing care, memory care options yourself, get to know the management and staff, well ahead of time. Find out which are well run, which should be avoided. Find out well ahead of time what availability there is, what entry procedures are. If the good ones require a deposit to get on a waiting list, consider doing so. Think if it as insurance, just in case.
Keep a bag packed so that in an emergency you just grab the suitcase and catch the next flight.
Finances are important - plan for the regular visits, and keep building savings for those difficult years, when you have to buy a lot of last minute tickets.
Finally - communication is key. Too often the consequences of ageing, illness, dying becomes the elephant in the room that no one wants to talk about. Even if you lived next door these would be very difficult conversations. An ocean apart makes it all the more difficult but it is critical to keep discussions going as to what your parents need, what you can reasonably provide from afar, and how to manage the gaps in-between.
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Not an easy row to hoe. I wish you and your parents all the very best.