Adding a smaller implant is possible and can correct your chin asymmetry. However, you should discuss the risks and benefits of adding another implant. An alternative method to correcting your chin asymmetry would be to remove the older implant and replacing it with one that is more appropriately sized. I shape and sculpt each implant to match patients expectations and fit your natural jaw line. It may be worthwhile having a second opinion from another specialize facial plastic surgeon, facial plastic surgery is an artistic field and different surgeons may advise slightly different treatment options.
Far more important than deciding if a tummy tuck or a mommy makeover is for you is the skill and experience of your plastic surgeon. Choose your surgeon rather than the technique and let him explain why one technique may be better than another and if you need a tummy tuck. Many board certified plastic surgeons provide a free first time consult and you should take advantage of that!
See the below link on some suggestions on finding the most qualified Plastic Surgeon for you!