Jennifer,
This can be a difficult transition. Hang in there.
We did the same thing - naps in big bed, crib at night. When this proved to be too challenging, we just took the crib away. We also opted to put a metal tension gate with a foot pedal on the bedroom door. This way, if "quiet time" wasn't a nap, we didn't have an escapee running around on the second floor. Many a nap (and sometimes bedtime) did we find our little one sleeping on the floor in front of the gate.
Two is young to transition, but we too had another baby that needed the crib.
My kids are 6 and 4 and STILL have quiet time almost every day - esp. over the summer! They don't have to nap, but they do read, color, etc. Something to settle down for awhile. My 6 yr old almost always naps. My 4 yr old hasn't much since she was 3.
I say put him down for a nap (with a gate up) and walk away. Make sure doors are locked or have childproofing and that any dressers or tables are secured to the wall with brackets (as he may attempt to climb). Finally, you may have to "clean out" the room of any electrical cords, unsecured blind cords, etc. as you have now ventured into TODDLERHOOD in his room...no more safety and convenience of a crib. You can put a sound machine outside his door if you think it will help.
I wouldn't keep sleeping/resting with him. Maybe right after lunch, read a nice quiet story and then walk out of the room. I read one time that if you don't let your kids' feet hit the floor after lunch you'll have more success with naps. Give it a try.
I hope this helps!
Sara