<<< looks kinda like a NanoHood (ExoTerra) , this hood should be fine in you small rearing viv provided you upgrade the compact to a 26W UVB200 and mount the hood UNDER THE MESH/SCREEN LID and about 8 inches above beardie's basking spot
To do this you may need to partly disassemble the hood to temporarily lift the reflector out (should be held in by maybe 4 screws (the NanoHood is , but not sure about your's) , drill a two sets of holes about 5mm diam in two groups of two (about 2 inches separating the holes in a group) , could do this without removing reflector but you don't know how the power cables are arranged under the reflector and risk drilling through these and it'll be easier to thread cable ties or twist ties through the holes to mount from under the mesh without the reflector in there. once the holes are drilled and the ties inserted ,replace the reflector and refasten the screws , install the uv globe , and then hang and secure the small hood under the lid using the ties (you might opt to use very short fat self tapping hexhead screws through a piece of rigid plastic sheet or off cut of timber wall board (if you have it handy) screwed into the holes you already have in the hood.
If there is a second 5%UVB compact in the dual dome , remove it, replace it with an ceramic heat emitter (mushroom shaped heater) ie
https://zoomed.com/repticare-ceramic-infrared-heat-emitter/
This is for use controlled at night and in really cold weather during the day. I highly recommend connecting the power cable for it's side of the dome to a switching thermostat like
https://www.ebay.com.au/i/281418169471?chn=ps&dispItem=1
(I use these and have found them very reliable , some have been in constant use for over 8 years),
essentially these switch the power on when under the set temperature (that you dialed up) and if the temperature goes above the set point by about 1 degC it cuts the power, I run my heatpads and control them 24/7 using these..
Keep the existing basking globe IF it is NOT COLOURED , it's in the other side of the dual dome.
Try to locate the Nanohood a close as you can to the dual dome (basking light side).
These are his lights.
UVB-Zoo Med FS‑C5M zml Bulb ReptiSun UVB Mini 5.0
And the basking light is also zoo med basking spot lamp.
Geez... Never trusting petsmart again! Thank you so much for taking the time to help.
His calcium is also zoo med (I see a pattern here...) called repti calcium, but they told me he didn't need anything else, but now reading the jar it says Without D3. Going straight to the pet store to purchase proper vitamins, thank you so much.