Welcome. My name is ***** ***** would be glad to assist.
Sorry to hear on the difficulty with the bulb socket.
It is very common on the halogen units and sounds like you have the GU 10 type bulbs, that pushes in and twists to lock in place.
They produce a large amount of heat and over time, the socket clips are distorted and even sometimes the wires become loose as well.
I do not know the exact fixture, as the model number does not come up in a database search.
Most times, it is very easy to just change the socket itself as opposed to the fixture.
Sockets are normally a few dollars.
Check how yours is mounted in the fixture and see if that is an option.
CLICK HERE to GU 10 socket.
They come in a variety of wire lengths and mounting, I am sure there is one available to match yours.
(do advise if the bulb is not the GU 10, I was going by the description posted)