I am fortunate in that the two grocery stores I frequent most are only a few hundred feet apart (though they are driving-distance away from home). So, I keep an Amy Dacyczyn-style price book and buy things almost entirely on sale wherever they can be had cheapest. Occasionally I will drive out to one of a few other stores for a third stop, but only if their online flyers indicate I can get enough groceries at a big enough discount to merit the gas. For example, a more-distant store occasionally has cheddar cheese at $1 less per pound than the best price I would get at my main two groceries, so I will go and get 10 to 20 lbs. As I have already judged the trip worthwhile, I will also pick up other odd items that are cheaper there that week.
I don't think anyone cares what your reusable bags look like. I have a huge mishmash of ones from various groceries and random giveaways (such as a payroll company, a CPE sponsor, DBF's automobile-based employer, etc.), and I see many other people with weird assortments.
Are you worried that someone might think you are stealing groceries? Maybe your best bet for that would be just to keep your receipts in your pocket, wallet, or purse so you can prove you did purchase the items if ever it is necessary. Or, make friends with the service desk staff and say "Hey, I've already done a bit of shopping from store #2, would you mind holding my cart behind the desk until I've purchased my groceries from here at store #3? I wouldn't want there to be any confusion about this."
Would it make sense for you to go to store #2 and store #3 on alternating weeks?