OK, so there are two aspects of this that can go one of two ways:
Your minion can be summoned, or else called, created, or whatever else.
Your minion can summon, or else call, create, or whatever else, its own minion.
As you can see, in both cases the difference is “summon” versus “something else.” This is because summoning has a particular rule:
A summoned creature cannot use any innate summoning abilities it may have
That means if you use summon monster V to summon a bearded devil, that bearded devil could not use its summon devil spell-like ability. By the same token, if you are fighting a real bearded devil, it can use its summon devil ability to summon another bearded devil (35% chance of success), but the second one cannot use its summon devil ability at all.
For everything else, unless it explicitly says otherwise, this rule does not apply.
If you create your minion without summoning (e.g. lesser planar binding, animate dead, and so on), then you have the real deal and that minion is able to use its own summoning abilities.
For instance, if you use lesser planar binding for a bearded devil, you get the real thing, not a summon. This is because lesser planar binding is a Calling effect, instead of a Summoning effect. The called bearded devil can use its summon devil ability just fine; its summoned bearded devil, however, cannot.
If you have a minion with a non-summoning form of creating minions (e.g. create spawn), then that minion can use that ability, whether it was summoned or not. So a shadow can use its Create Spawn ability, regardless of whether it was summoned via summon undead V (Spell Compendium) or created permanently via create greater undead.
Assuming you control your minion, and your minion controls its minions, you can effectively control your minion’s minions by ordering your minion to control them in particular ways. However, you do not have direct control over these minions, which means if your minion that you were using as an intermediary is removed from the picture, you have no control over its minions.
So, if you did summon undead V for a shadow, and it used Create Spawn, and then summon undead V’s 1 round/level duration ran out, you’re left with a spawned shadow that you have absolutely no control over.