Q:

How difficult would it be to make things out of glass at home, using a solar reflector?

With a solar reflector/concentrator that was a square metre or two in size, I would expect it would be possible to get temperatures high enough to melt glass, even if only for a small sized object. 
What (high-level, no great detail required) technical hurdles would need to be overcome to be able to make something useful out of used glass containers at home?

A:

I studies Physics in the days when a Physicist made their own equipment; a mandatory subject was scientific glass blowing.
There are various kinds of glass. The main type used for ordinary bottles and such is soda glass. This answer will focus on this glass.
Soda glass can be worked (from memory) at around 600°C. So if you had some glass rods or tubes, you could heat it to 600°C, and just join them together. More on that later.
But to completely reuse the glass, it needs to be properly melted. For soda glass that means 1040-1090°C.
The liquid glass could then be cast, but a cleaner result is achieved by blowing or using various shaping tools. To blow the melted glass, it needs to cool to a working temperature of around 900-1000°C.
As mentioned above, the glass can be worked at lower temperatures.
After any heating, the glass item should be allowed to cool slowly; this is called annealing. It's purpose is to relax the strains in the material that are caused when one part has been heated more than the rest. Improper annealing usually results in the item cracking.
Usually, one would use three furnaces. One for the melt, one for reheating work between steps, and an annealing furnace where the temperature is gradually reduced.
Since the material is at a high temperature, safety precautions must be taken. Firstly, the worker must understand the treatment of burns, and the use of protective equipment. One learns quickly to never handle the work with bare hands until it is quite cool. Leather gloves, steel tongs, shears and blowtube, and a steel work surface are all required.
Since most small scale glass work is carried out using gas torches, the use of a solar concentrator would require an additional learning curve.
So, to answer the question: if you don't have the equipment and knowledge - quite difficult. But IMHO certainly possible.
Useful Wikipedia references are the physical properties of glass page and the Glassblowing page.

A:

Energy input for a given crucible is the main factor.
You need energy input to exceed losses from radiation, and some convection and minimal conduction to give net energy gain so temperature will rise. While notionally you can achieve this with as little energy input as you wish, in practice it helps to have a healthy net energy input so that losses are swamped by energy gain. 
As an indication of the energy levels available, 
The typical Sky TV dishes - ovals about 600mm tall, when covered with mylar aluminsied foil can create enough solar concentration to set your house on fire. Ask me how I almost know* :-).   
A 1.8m diameter circular satellite dish has an area of about 2.5 m^2.
Maximium midday sun on that is about 2.5 kW of power. Cover the dish with aluminised mylar and you can get say 1 kW plus thermal output. This can be concentrated in about a 100mm sphere at the focal point. (Exact size depends on dish geometry and covering precision but can be small.) With 1 kW avA crucible with a black outer surface could be made hot enough to melt glass - or a range of metals . 

Solar house burner - almost:
*-OR a chair on the back porch. A satellite dish was doing double duty as a cellphone repeater access antenna - place cellphone on arm at focus point, and for solar experimenting. Lefton a chair arm after a night time cellphone call, thge early morning sun was focused on the chair arm. Loss of house was a possibility. Notre smoke still rising on left side of image. 

The following relates to Microwave Oven glass melting, not solar, to give an idea of the power levels needed:
PPP: Glass Fusing in a Microwave Oven

Making glass jewelry is fun and will teach you the principles of glass fusing. With practice, you should be able to achieve consistent results in microwave firing. You will need a microwave kiln, which is a small ceramic fiber container that fits inside the microwave oven. The microwave kiln captures microwave energy and concentrates it in the firing chamber. The concept is similar to using a magnifying glass to focus sunlight. 

The biggest challenge to microwave firing is the fast heating rate. A microwave kiln reaches 1650°F (899°C) in only 5-10 minutes. Firing times depend on the wattage of the microwave oven; the lower the wattage, the longer the firing time. However, firings can be controlled to achieve consistent results. 
Making glass Jewelery in a microwave oven
HOW TO USE A MICROWAVE KILN TO FUSE GLASS JEWELRY & PROCESS LOW-FIRE PMC ART CLAY SILVER. DOMAIN MICROWAVEKILN.COM & MICROWAVE-KILN.COM ARE FOR SALE

