Iron Man 2 saw James “Rhodey” Rhodes take Stark’s silver Mark 2 armor and with the help of Justin Hammer (Sam Rockwell) turn it into the heavily armed War Machine. For Iron Man 3, Marvel Studios took some ideas from the comics and used them to drastically change the appearance of Rhodey’s duds into the Iron Patriot. - Screen Rant on War Machine
Tony Stark doesn't seem to be into the practice of sharing his best technology/inventions with the US Government. My question is, why didn't he take his armor back from Rhodey?
He could have perhaps:
Hijacked the suit's computers remotely
Gone in with his own suit to take the Mark 2 suit by force when not being worn.
“When last we saw Jim Rhodes, played by Don Cheadle, he was flying away from Tony at the end of Iron Man 2 wearing the Mark 2 suit that he had taken from Tony’s house. What we learn in the beginning of Iron Man 3 is that they’ve made an arrangement. Tony has let Rhodey have this suit; he’s using it in conjunction with the US Government..." - Marvel Studios President of Production Kevin Feige
If this is the case, when & why did Stark make that agreement?
It doesn't appear, based on the films, that Stark and Rhodes made such an agreement, rather it's inferred from the beginning of Iron Man 3
Again, Tony doesn't seem like the type to share his weapons with the government; In fact he is, if I understand correctly, not happy about having designed and sold weapons in the past.