Could a Compression Garment have Negative Effect on Hips After Brazilian Butt Lift?

I am not sure what you mean by second stage which could mean a second surgery or a second compression garment. Here are my general recommendations and my rationale:

Compression Garment Instructions and Purpose after Brazilian Butt Lift and Liposuction:

Most important is to follow your surgeon's advise. He/She has specific reasons for their recommendations. In general this is what I recommend to my patients - wear their garments for a minimum of 3 weeks full time then for 12 hrs (day or night). if not a lot of redundant skin following liposuction to a maximum of 6 weeks. To be effective the garment needs to fit snug but not too tight as to cause pressure problems (inspect your skin if discomfort and when skin is exposed), or prevent you from sleeping. As the edema resolves it is common for patients to switch to a smaller garment that fits - A Spanx type garment would work rather than ordering one or paying more at your doctor;'s office.
Following Liposuction and Fat transfer procedures used in the Brazilian butt lift,  the compression garments are required for three main reasons:
It restricts the amount of edema that forms and hastens its resolution by mechanical pressure
It decreases the amount of bruising
It assists the loose skin in retracting or shrinking in the liposuction areas
The length of time that the garment is worn varies dependent on the amount of fat removed, the elastic nature of your skin, how much loose skin remains at the liposuction site or how much swelling from edema in the buttocks you have and other factors. Your surgeon would give you the best advise. However in general this is the routine for my patients.
The first garment should be fitted for you in the office prior to surgery and applied in the operating room. Often it will become loose as the edema is mobilized and then it will need to be replaced. Spanx is a reasonable compression  garment if it gives enough support and is the right size. I have my patents bring them in and confirm that it fits well.
Most important advise is to listen to your surgeon's advice as he best knows how much fat was removed in the donor sites and transferred into the buttocks, and other factors mentioned above

Compression garment may or may not be necessary after liposuction, depending on which area of the body liposuction was performed. If you are having your hip area liposuctioned for Brazillian buttock lift, then I would have you wear a compression garment for the hip area.  If you are having your hip areas augmented with fat graft injection, then, I would not recommend wearing a compression garment at the hip hip/thigh region. Second stage compression garment to me means at least three to four weeks out, wearing a very light compression type of garment for support. What would be more important during your postoperative period would be gentle massages at the area of grafting and areas harvested, to help smooth out any possible lumps or bumps.