First of all, there are many happy 22-250 owners here, myself included, mine shoots great with handloaded 50gr Vmaxes.
The fired cases won't fit back in the chamber because they're too hot, or as Fred said, there's excess head space from either a poorly fitted barrel or too deep a chamber, this has been a common problem reported before for the 22-250 even with factory ammo. If you look across the barrel to standing breech joint after the shot before breaking it open, you'll see a gap between them at the top, a sure sign of something wrong, the hard to release button is the second sign, if there's no gap, you may be able to lap the latch and shelf smoother by applying a metal polish to the shelf, close the action and work the latch button...... until your thumb falls off!!!
Then clean it up and see if it still does it, H&R is always available to make repairs if it doesn't help, but I'd definitely try different ammo first.
Pop opens are usually caused by ignorance(lack of knowledge about Handis
), easily fixed, as usual see the FAQs.
Tim