Like darktrain wrote while I was typing this, the cable you linked to is what you will want. The 1/8" TRS Stereo output of the Ugly and the M10 is by its nature an unbalanced set up. There is no way to wire a single unbalanced stereo TRS jack to two balanced TRS jacks without additional circuitry. A balanced connection requires 3 wires (+, -, and Shield). The unbalanced sources you are using only have R+, L+, and shield. To have a truly balanced "differential" signal you need the L- and R- signals.
Beyond the scope of this discussion, if you know the output impedance of the unbalanced M10 and Ugly circuits, you can make a passive impedance balanced cable that could help reject noise on the cable, but it's a custom made item and not worth the effort IMO. The signals would still be single ended (not differential) but the impedance would be balanced which is important for rejecting noise.
The MOTU will accept unbalanced TS inputs just fine and the cable you linked to has the correct color code. Tip = Left = Black, Ring = Right = Red. I'd go with the 3' model if it works in your rig. That way you keep the unbalanced runs as short as possible. Ted and darktrain make high quality custom stuff at any length you specify.
I love my Ultralite mk3!