I've been to Sweden pre-babies and I've taken my kids to the West of England. I lived in London for 6 years (also long before I procreated) and I took the train from Amsterdam up to Stockholm to visit that city. I have distant cousins in another Swedish city but haven't managed to get up there to see them. It's on our to-do list...

I would vote for the latter just because of time and space. Sweden is nice but the distances are far. My kids are not good in the car for long periods.

England is more compact and there's so much to do with kids (much of it weather-permitting). You also wont have any language issues, although there are some differences. My children enjoyed watching T.V. in the accent and reading the signs in England. Your older one might start to make literary connections (depending on what she's read and where you visit). For the record, my kids BEG to go back, they loved it so much.

The North is beautiful but mine enjoyed the western region (we were around Bristol and Bath). You could continue on to Cornwall but be wary of the "holiday traffic" on the weekends when people leave/arrive.

If you fly into Heathrow, you can take the Reading Rail link bus from the airport to Reading station from where you can catch a train going basically anywhere in that direction. I would recommend getting a bit of a rest and a break from a day's car rental and stay in some easy-to-reach town for the evening. As you probably already know, transatlantics arrive in the morning so you would have plenty of time to do this and it's really easy. No reason to stay in the London area that night or even go into London to catch the train.

Just as a tip, British schools let out really late, in July. If you can schedule yourselves to arrive in June, that would work out well, as far as crowds and prices are concerned. By contrast, Swedish schools get out earlier, about a week after U.S. schools usually do. They don't get a lot of vacationers up there and crowds will not be a problem. In fact, a lot of families actually leave on vacation, earlier than in most of Europe. Another plus for Sweden would be the novelty of the long days. Stockholm has a two hour, never really dark night that time of year. Try to get there for the Midsummer Day holiday with the Maypole dancing (yes they forced me to do it). Just hope you don't step on as many feet as I did!

Both are great destinations. Research prices and weather (I don't think there is much contrast to either) and other factors before deciding.