Taking This in Steps

• A creature is in a stance until it takes a swift action to change its stance.

• While in the 1st-level Shadow Hand stance child of shadow (ToB 76) "[i]f you move at least 10 feet during your turn, you gain concealment against all melee and ranged attacks until the start of your next turn. You also gain the standard benefits of concealment, but you cannot use this stance to hide in plain sight...."

  Here's all about concealment

  Concealment Miss Chance
  Concealment gives the subject of a successful attack a 20% chance that the attacker missed because of the concealment. If the attacker hits, the defender must make a miss chance percentile roll to avoid being struck. Multiple concealment conditions do not stack.

  Concealment and Hide Checks
  You can use concealment to make a Hide check. Without concealment, you usually need cover to make a Hide check.

  and that's different from

  Total Concealment
  If you have line of effect to a target but not line of sight he is considered to have total concealment from you. You can’t attack an opponent that has total concealment, though you can attack into a square that you think he occupies. A successful attack into a square occupied by an enemy with total concealment has a 50% miss chance (instead of the normal 20% miss chance for an opponent with concealment).

  The stance child of shadow doesn't give the adept total concealment or make the adept invisible; those are different effects. The stance's effect just gives him an opportunity to use the Hide skill to hide and a 20% miss chance versus melee and ranged attacks.

  The DM must decide what movement the stance child of shadows requires. I would argue anytime a creature has gone from one square to a different square it has moved, but stricter interpretations--such as limiting them to actual movement modes (i.e. burrow, climb, fly, swim, and land Speed)--are equally reasonable. Jumping should qualify under either as part of a creature's land speed.

  If movement places a creature in weird position, the standard means to determine if the creature has concealment apply:

  To determine whether your target has concealment from your ranged attack, choose a corner of your square. If any line from this corner to any corner of the target’s square passes through a square or border that provides concealment, the target has concealment.

  When making a melee attack against an adjacent target, your target has concealment if his space is entirely within an effect that grants concealment. When making a melee attack against a target that isn’t adjacent to you use the rules for determining concealment from ranged attacks.

  This means while it might be weird and unexpected for the defender to find the attacker suddenly on the ceiling above him--and might entitle the attacker to a bonus to attack rolls for having higher ground--, the target will notice him unless the lines drawn don't allow it or another effect intervenes. It's D&D, and folks actually do check ceilings for enemies.

• A creature then takes a swift action to change his stance from the stance child of shadow to the 3rd-level Shadow Hand stance assassin's stance (ToB 76) is eligible to inflict +2d6 sneak attack damage (PH 50).

  The adept using the stance assassin's stance is eligible to inflict that sneak attack damage if he meets sneak attack's conditions: Is the target denied his dexterity bonus to Armor Class or flanked? If he is either or both, then sneak attack damage applies. As @TheXenocide noted, by itself, although counter-intuitive, neither concealment nor total concealment meet sneak attack's criteria so another method of meeting the criteria must be used. I suggest blinding the creature or turning invisible.

  This question addresses using concealment or total concealment in combination with sneak attack in greater detail.

Trip would go from cheap to worthless

The long-term issue would be diminishing the value of tripping. At low levels, PC's have precious few resources, so making trip less valuable means that it will see less play. That riding dog is a threat in its own right at 2nd level, but it cost some of the bard's gold. By even 6th level, the same dog is nearly useless; it's relatively fragile, and it's relatively weak.

Recommended Solution

I suggest mirroring how the Withdraw action changes merely leaving a threatened space. Thus it could be named Defensive Stand, or whatever, and be a full-round action, unless the creature is limited to a standard action (as with withdrawl, a nauseated creature couldn't perform this action) to stand without provoking Attacks of Opportunity.

This way any creature can take a move-action to stand, risking an Attack of Opportunity, but by taking a Full-Round action to stand, being properly cautious, they provoke no Attack of Opportunity. That way trip retains most of its value for wasting actions, and some creatures (low-no intelligence, or very aggressive ones) will still stand faster and provoke the attacks.