Tips for getting the wheel back on?

[laura*]

It likes to hang up on the brakes (easy)

Are you releasing the brakes? Many brake mechanisms have a way of temporarily releasing the brake cable's pull allowing the pads to swing out, thus clearing your tire. Mountain canti's and V-brakes will unhook, while road calipers may have a lever to twist.

Instead, it's almost like the dropouts are catching on the "screw" parts that correspond to the quick release and the cone-nut-thing.

Perhaps your frame spacing is slightly too narrow? Some frames need to be gently spread to fit a wheel back in.

Does your quick release have the two springs? (Narrow ends toward the axle ends, wide ends toward the QR mechanism and nut.) These springs push the QR parts away from the frame dropouts.