A few things about camping up near Chambers Lake:
This area typically doesn't open up until mid to late June due to lingering snow, so if your plan is mid-June, I'd call the district ranger station just before you go to see what the status is.
One can often be treated to seeing moose in some of the swampy areas along CO 14 or on the Laramie River Road.
There is some dispersed camping in this area. Check along the Laramie River Road. There are also designated dispersed camping sites on the road up to Long Draw Reservoir.
Here is a map showing dispersed camping restrictions. Again, snow might be an issue in mid-June.
Mosquitos can be a problem up there with all the standing water, but we find that generally isn't an issue until July when most of the snow is gone.
As for the Wyoming portion of your trip, are you planning on driving the Snowy Range Scenic Byway (WY 130)? Well worth the time to drive it, although the upper parts may still have snow closing the CG's in mid-June. There are NFS CG's on the lower elevations on either side that should be open at that time. Amazing scenery along this drive.