Revision Lower eyelid retraction surgery
Canthoplasty alone will not work for you. You need internal eyelid support and modified cheek lift in order to raise the lower eyelids. This is a complicated procedure that should be done with a specialist. See my website for more information.
I commonly perform this type of repair in my practice.
In my opinion, even a lateral canthoplasty with a hard palate graft will not be adequate to repair your issues. The reasons for this has everything to do with the shape of your lower bony orbital rim. This is precisely why you need more than just eyelid surgery with a hard palate graft. I recommend a hand carved ePTFE rim implant that augments the orbital rim and helps support the cheek soft tissue at the orbital rim. Then the lower eyelid reconstruction with a hard palate graft will be successful. Study my free ebook on eyelid surgery cited below. My website also has many before and after pictures of this.
Your eyelid is low laterally on both sides. The canthoplasty was done to correct this. You may have something called mid-lamellar scarring now. This occurs after lower lid surgery, and when you push up on the lid it won't move up. When you have this you need to put some sort of graft into the lid to allow it to move up or you will be low again after the next surgery. A graft is taken from the roof of the mouth to provide the extra tissue. ALternatively an artificial graft can be used, but results are not as predictable. These corrections are not easy. He is well trained in this sort of surgery.
Lateral canthal dystopia
Assuming your goal is to elevate the lateral canthal angle, correction of the position of the angle would involve - repositioning of the lateral canthal tendon (LCT) higher on the lateral orbital rim by roughly 0.5 cm. There is a reason that two previous procedures have not provided long-term results - and I believe that reason is a deficiency in the lateral eyelid skin. To access the LCT, an incision in the subciliary location would be a good approach. Once the LCT is elevated, the skin is likely to be retracted/ deficient in the lateral lower lid, and excessive in the lateral upper lid area. I don't believe that the lateral canthus will stay elevated in a good position unless you have the skin augmented in the lower lid. A transposition flap would provide long-term elevation, with the advantage of rearranging skin in that area rather than grafting. Different opinions may be very confusing - and I would suggest getting multiple opinions "up front" rather than after another procedure. Make sure that you are comfortable with recommendations prior to going back to the operating room!
Lower eyelid droop
It would appear that this patient has an inherited negative tilt of the eyelids. The usual anatomy is that there is a slight downward tilt from the lateral to the media (outside to inside corners) of the eyelids. This allows the tears drain toward the nose and into the lacrimal sac. This patient has an inherited tendency for this to be reversed such that the tilt is downward toward the side of the face. Having had two surgeries to correct this already it is appropriate for the patient to go to an eyelid surgeon who has considerable experience correcting this. She has had recommended another canthaplasty, but it may be advisable to use a different approach.