My personal tips, are:
1. Don’t stress! Avoiding cross contamination is not difficult. You just need to be pro-active.
2. If the allergies in the family are severe, keeping two separate sets of cooking utensils and pots or pans is one way method to use. Have different styles and colors of each so you can easily identify which ones you use for regular cooking and which ones you use for the allergy cooking. So, for example when I make eggs for the rest of the family using a little bit of butter (which they prefer), I have a larger egg pan which I use to make their eggs. On the burner next to theirs I use a smaller pan to make my egg which I usually cook with olive oil.
3. Another thing you can do either in conjunction with or instead of having two separate utensils and pans for everything is simply to wash things in hot water and soap in between the uses. Whenever I’m cooking for someone with a peanut allergy which happens to be one of the few food allergies no one in our family currently has, I first wash everything I’m going to use for baking or cooking in hot, soapy water and dry them with a clean fresh towel even before I begin cooking. Numerous studies have shown that any contaminating residue from what you’ve cooked before is definitely washed away with a good scrubbing in hot, soapy water.
4. A third method you can utilize is to invest in parchment paper which I use all the time. It’s great because you can line your cookie sheet or insert it in your tube pan or put it on your casserole dish for any cooking or baking and then simply remove it, which keeps the food from contaminating your pans. During the holidays when I have to bake all sorts of different items — gluten free, egg free, sugar free, nut free, etc… — along with traditional baked goods, the parchment paper comes in very handy as I simply remove and reline with each different goodie I’m baking.