How to Remove or Improve Facial Scar on 2 Year Old?

It is common for scars to fully mature for up to a year. In the meantime, there are a few things that may help to ameliorate your incision/scar. The most proven (as well as cheapest) modality is simple scar massage. Applying pressure and massaging the well-healed scar has been shown to improve the appearance as it breaks up the scar tissue, hopefully producing the finest scar as possible. Other things that have been shown to add some benefit, albeit controversial, are silicone sheets, hydration, and topical steroids. In addition, avoidance of direct sunlight to the incision will significantly help the appearance as they tend to discolor with UV light during the healing process. If unsightly scars are still present after approximately a year's time, other things that your surgeon may consider are intralesional steroid injections, laser, or just surgical revision of the scar itself.  The scar itself will never go away, but hopefully one, or a combination of these above, will improve the appearance.  I would await until after she has been done growing to consider surgical scar revision.Hope that this helps!  Best wishes!

These types of scars on the cheeks can be improved with fractional laser and pulsed dye laser as the best two options.  

It would be best to wait 1 full year to see how much the skin and scar remodels itself; no doubt it will improve with time alone (sunscreen is important too). Massaging the scar and silicone gel sheeting is modestly helpful.
Hard to say whether stitching it up from the beginning would have been better, so I wouldn't beat yourself over that. I would meet with a dermatologist or plastic surgeon to discuss the treatment options now and for down the road (some procedures can't be performed on a squirming toddler).

Unfortunately, a scar is permanent and cannot be erased or improved.
Moreover, at this time in its healing, you have to wait and see how it would turn out. Over the next 8 months, the scar will constantly re-model itself until it takes it final form. Only at THAT time will you know how the scar looks.
If you think the scar looks horrible once it matures, you may consider having it worked on. That would involve operating on it, removing the old scar and trading it for a nicer scar.
Personally, I would not do it until her growth spurt is over and only if she is emotionally bothered by the scar. As much as you may be bothered by the scar now, it WILL look a lot better. If your daughter is not bothered by it, I would leave it alone.
Dr. P. Aldea

Even if she had stitches, there would still be a scar. As Dr. Aldea has said, massaging the scar with VitE or Mederma will help and you should give it a year and then have it looked at by a plastic surgeon. Most of the time, no revisions are needed. Remember that scar revision is not scar removal.