The truth is, Use Scroll is an emulate class feature check. You are in fact emulating the class feature of spellcasting ability, at a caster level of your UMD roll minus 20. The description for use scroll is just an easy way to do the math quickly. Result is the same either way.
The other thing that it matters for is a check to use a staff. This is also an emulate class feature check. If your effective caster level is above that of the staff, you get to boost it's power to your effective caster level.
Use wand is an emulate class feature check as well. A caster level of zero is sufficient to cast from a wand or staff, IF you emulating the class feature. The only way to have a caster level of zero and the class feature is a UMD check, since the other way to get the class feature gives you a caster level of 1.
You only need one roll to use a scroll, and two if your ability score isn't high enough. No third roll is ever needed.