It was extremely common before, which is why the aforementioned law was passed. You would've had to do the USMLE to apply for residency positions through the Match, but this isn't relevant with this new change.
For peds I imagine it wouldn't be too hard getting a position (if you've done 5 years of training in the UK as above, more likely a fellowship which would be slightly more selective otherwise) as it's a somewhat undersubscribed specialty as I understand, in a hospital. No idea how difficult it would be in a private clinic...however if you're willing to work in a more GP/family medicine oriented manner in a rural practice area there are many opportunities (NB rural here could range from central Maine to Hawai'i so...a fair bit of variety. You'll be far from any cities though, you can bet on that).