Well ...
Here's the dilemma.
If you have a 10 gallon refugium hooked up to an overflow from your 44 gallon tank, and you plan to put a return pump in this refugium ... you must isolate it from the algae and sand/live rock in the refugium. Otherwise the pump will suck stuff up.
If you do isolate the return pump in this 10 gallon tank, and use a pump with say 300 gph, you'll pump 300 up to the tank, and get 300 back to the refugium. That's a lot of flow in a 10 gallon refugium. Plus you must allow for a rise in the refugium when the pump turns off - some amount of water will drain back to it from the main tank (until the siphon is broken ).
So you're 10 gallon refugium may only be able to normally operate at say 5 gallons of water.
And when you turn the pump on - I'm afraid the water returning to such a small refugium will stir everything up - and not allow you the full benefits of having the refugium.
If you choose a very low flow pump, you can overcome this high velocity water draining back down from the overflow, BUT you may find that you don't have enough flow through the U-Tube ... air bubbles may accumulate in this U-Tube, and eventually cause the siphon in the tube to quit.
Then you have BIG problems.
Ideally - the installation of a separate SUMP and a REFUGIUM is the best, or at least have a dual sump/refugium single vessel.
A place for the pump, and a place for the refugium stuff.
You avoid or at least eliminate the chance of many of the above pitfalls and potentials for disaster.
By having a sump - you can run the overflow at near capacity, use a good sized return pump, get a good turnover of tankwater which aids in circulation and air exchange, adds a measureable volume of water to the total system, allows you a place to put your heater and other equipment ( skimmer )and let's everything run full blast.
But you must have a way of tying the refugium into the system.
How much room do you have under your 44 tank/stand ?
Have you explored using Rubbermaid type containers ?
Could you fit a 20 gallon or larger tank under your stand ?
Do you have anywhere else you could locate the sump/refugium rather than under your tank/stand ?
It's pretty easy to set up a sump and refugium using different approaches.
I, as well as others here, would be glad to help any way that we can.
Just let us know - okay Chris