Advice or experience living in 2 or more countries with toddlers

You might be interested in the fb group:  https://www.facebook.com/groups/worldschoolers/

We did this with two toddlers, and later an infant. It's very do-able. We lived in the Bay Area and then in NYC, then expanded to Barcelona. The following year, we did the same thing, but in France. When we lived in France, we traveled. I'd recommend staying put in one area and doing day and weekend trips from there. That way you also get a better sense of the community. Places I thought were toddler friendly: 

Madrid, Barcelona and Valencia. I liked that you didn't really need a car, there was the beach or city and expats from all over the place. We did a school in Barcelona but due to schedules, we ended up doing local meetups and playgroups. They're not too hard to find. Maybe now, in the time of CV19. 

France was easy for us because we have family there. I think I would have found the extreme weather of Paris during winter to be a little more difficult with three kids, but hey, Parisians do it so I guess I could have done it. I preferred Toulouse and Montpellier to be easy to get around (my biggest struggle with three younger kids was getting from point A to B with some sort of straight line). Nice was the best place to be for weather and beaches, but the driving and parking made me go a little crazy. There are also meetups in France. 

Now that my kids are older, we live half of the year in Puerto Rico and the other half in the Bay Area. We love that arrangement. It's almost too easy with kids! The biggest challenge for us was the criticism we received from family and friends (lack of roots, what about giving them a steady life, learning new cultures all of the time is intimidating....) We kept going and don't look back. Our kids seem to be happy thus far. Feel free to message me privately if you have questions. 

Due to my husband's work, I spent a summer (pre-COVID)  in London with two boys aged 4 and 8. It was awesome. The boys had a blast walking around everywhere and visiting museums every day that hosted multiple events. Because of the same dilemma as you face now, we decided to come back right before the start of school. To maintain his job, my husband was commenting to London on a plane and I was staying in Berkeley with two school children.

We're sort of trying it out right now.

We left the Bay Area mid summer with our toddler and are currently living abroad (not Europe though). We elected to not to enroll our child in the local school when we first arrived due to covid, but in this country, education is considered a human right, and our child would be allowed to enroll even though we are not citizens or permanent residents. We have a private school in mind because it offers more flexibility, and also I don't feel right taking public funds when we haven't contributed. Our child will be starting school in a couple of weeks.  If not for COVID, school would have happened for us already.

Drawbacks - it's a bit lonely for our child without school, but I imagine it would be the same had we stayed in our overpriced Berkeley apartment and the preschool closed (or zoom).

Biggest obstacles/challenges - honestly, this stupid COVID thing the biggest challenge. Our child makes friends easily, but with covid, there's so much weariness that we don't socialize as much as we would otherwise. We also came without all of our "stuff", so there is not a lot of toys, musical instruments, or books. We entertain ourselves by doing stuff outside. Had we planned better, we would've arranged for some of our items to be shipped here. But we put them all into storage.

Benefits - I'm very excited that when we enroll our child, there will be easy exposure to several new languages. The teachers instruct in the "official" language, but the kids have different backgrounds and she says they all start to pick up each others' languages after awhile. Depending on where you move to, you will probably save money on rent.

In short, it's definitely possible! We are extremely fortunate that my work allows me to be remote, and for tax purposes I am just on an extended vacation and still a California resident, so it's not so complicated tax-wise. We made the decision to leave, picked a country and went for it. Getting on that plane and leaving allowed us to finally BREATHE.  We are not looking forward to returning. We'll see what happens when the time comes. 

We haven't done this but some good friends of ours did, splitting their time between the U.S. and Japan starting when their kids were little. Initially they were in Japan most of the time spending only 2-4 months a year in the U.S. When their older child was in 1st grade (age 6), they started spending more time in the U.S. They were generally here for the start of school then left mid-November until mid-January. Their kids went to school in Japan during that time. They came back and their kids went to school in the U.S. until mid-May when they went back to Japan and their kids went back to school again there. The mom, who is Japanese, would spend more time in Japan with a kid who needed to be there more because it was an important year of schooling or whatever.

Once the kids hit middle school, they went to Japan a little less but still probably spent 3-4 months a year there. When the older hit high school, they had a serious discussion about whether they should send the kids the rest of the way through school in Japan. They had settled on staying in the U.S. until covid hit, at which point they packed up and moved to Japan. The older child is now a junior in high school and may come back to the U.S. for his senior year to say goodbye to his friends. The younger child is in 9th grade and plans to stay in Japan through at least high school.

The children are delightful. Here they have lots of friends and do well in school. According to the parents their lives are similar in Japan. The older child has started some businesses which rely on him being bilingual and bicultural. I am jealous and wish our kids had the same experience.

Two things that helped the parents are that they have a company so could live anywhere and had a house in each place (with grandparents nearby) so the kids truly felt like they belonged in both places. I think the grandparents nearby was helpful for bits of help (could you gather our mail when we are gone) but I'm sure you could get friends or a company to do stuff like that.

So jealous for you and your kids!