I think this is the best analysis. Making and selling a product [your purse] that displays -- in whole or in part -- one or even two other company's trademark is likely an infringement of those marks. But more than two moves much closer to non-infringing use. As all have said, only your own attorney can provide you with an opinion based on your particular purses.
There may be the potential for patent protection, either utility or design, so seeing an IP attorney would be a good investment for you. Also, there may be potential for a brand name you could protect. An IP attorney might help you with that, as well.