Most airlines will allow you to bring on one piece of carry-on luggage (sounds like your weekend bag) and one "personal item," which can include backpacks, purses, briefcases, etc. If your large purse will fit under the seat in front of you it should be fine. Size limitations for the carry-on suitcase vary somewhat by carrier, so check with your airline for specific details to see if your bag fits their size requirements.
Sun tan lotion in a container less than 3.4 oz. can be carried in your carry-on bag, but must be in a 1 quart zip-lock bag with all of your other liquids and gels (which also must be 3.4 oz or smaller). Each passenger is allowed one bag and it must be removed from your carry ons at the screening checkpoint.
