Adding to your cons list: Relocation is one of the most stressful life events - relocating internationally even more so, and small kids amplifies if even more. In addition to 'culture shock' issues already listed on this thread, there's a ton of logistical details that add to the stress. If you take some of your stuff with you be prepared for issues with the shipping company and customs. In our case we ended up living out of our suitcases for about a month while we waited for our shipment to clear customs.
Whatever you don't bring with you be prepared for the sticker shock - goods in the EU are expensive and the ~18% VAT doesn't help. In many parts of the EU an "unfurnished" apartment literally means totally unfurnished, as in you need to provide all your own appliances, fixtures, etc. - this means you need to install your own kitchen and bathroom, lights, yada yada. Not only is this spendy, it's a major hassle, and in these places furnished apartments are very expensive. So look into what the norms are for apartments in the area you're considering.
You will also need a EU bank account to rent an apartment because your landlord is unlikely to accept a paper check because electronic wire transfers are the norm, and because of banking regulations you can't easily transfer money from a US bank to your EU landlord. In fact, getting money transferred from the US to the EU in general is a pain. If possible, set this up in advance and get Euros in a EU account in advance of your move.
Then there's the joy of taxes. Because the US is so worried that some wealthy fat cat might move overseas to avoid paying their fair share, the US is one of the only governments in the OECD requiring citizens to pay taxes on their global income. Not it's not as bad as it sounds, because most (all?) countries in the EU have tax treaties with the US (basically, you pay the highest of the two rates), but it does mean you have to continue filing taxes in the US while living in the EU. But the fun doesn't stop there, because of the way the tax treaties work with one affecting the other and vice versa, and because the two countries very likely have different filing deadlines, this means you likely have to amend your filings with both countries. Basically, you get to file 4 times each year - the short of it is you're going to spend a lot of time with a professional tax preparer each year.
Then you have to find schools, doctors, dentists, etc. etc.
The first 1-2 months are occupied with these types of details, which is offset by the excitement of exploring what a new country has to offer. Homesickness sets in around month 2 and continues for a number of months (4-6?) - this is a hard time - there's a continuous low-level of background stress because you don't quite fit in and even little things can be difficult to figure out (how do you winterize your car, where to go, what is expected? And other things like this).
After about 9+ months things settle down and start to feel more fun and relaxed again. At this point life because just life again.
Is it worth it? It's difficult to say. If living overseas is a goal of yours then it's probably worth it, even if it pushes FIRE back. It's an opportunity to really live like the locals in a way that's not possible if you're just traveling through. It will change your perspective, broaden your horizon, bla bla. But it's a shit ton of work, stress, homesickness, and such.