My son has a dairy allergy and he has avoided dairy 100% for the last seven years. Kosher dairy items DO still contain dairy. Only Kosher meat or parve items will be dairy free. Do not rely on a kosher label alone to think it's dairy free. You will have better luck with items that say Vegan or dairy-free. Looking at kosher items is most helpful for me when I'm choosing a meat item, like hot dogs or lunch meat, as no kosher meat product will ever contain dairy.
All of the dairy-alternative products we buy are in our local grocery stores - Ralph's (part of the Kroger family), Sprouts, and Whole Foods all have a good variety. Even Target has some now.
We use Earth Balance "buttery spread" (margarine) instead of regular butter. It's available in a spreadable tub and also in sticks. Fleischmann's unsalted margarine sticks are also dairy free (but the salted variety are not). It is not true that there is only one dairy-free margarine on the market. We used to use Smart Balance, but discovered Earth Balance and prefer that one.
For yogurt, my son likes the So Delicious brand, which makes both soy and coconut milk yogurts. He used to eat the soy, but more recently started preferring the coconut milk. The same is true for this brand's ice cream.
For cheese, we have found Daiya shredded cheese to be the best for melting, so we use it in things like pizza or lasagna. Please note that A LOT of soy cheeses still contain either casein or whey (the other protein that causes a lot of dairy allergies), so you need to read the labels very carefully.
We keep our cupboards stocked with dairy free snack foods, many of which are totally common items: Wheat Thins, Ritz, Z bars (several flavors but not all), Orville Redenbacher's "simply salted" natural popcorn, Fig Bars, Nature Valley granola bars (some flavors), animal crackers, and many many more.
For baking, the Ghiradelli DOUBLE chocolate brownie mix is incredibly delicious and completely dairy free. The triple chocolate mix is NOT dairy free. Ghiradelli semi-sweet chocolate chips are also dairy free. Even Duncan Hines cake mixes (many but not all) and frosting (most) are dairy free.
For cream cheese and sour cream, we buy Tofutti brand "better than cream cheese" and "better than sour cream."
I recommend baking cupcakes and freezing a batch (we freeze about a dozen at a time) so that you can bring one whenever you go to a birthday party. We also keep frozen pizza on hand, as most bday parties serve pizza. Daiya brand and Amy's brand make good dairy free pizzas (for Amy's, you need to find the one that says Cheeze, as not all of them are dairy free).
The whole things takes time to figure out. It can be very scary and frustrating in the beginning, but it is SO much easier now that he's eight years old than back when he was a toddler/preschooler. Make sure your friends and family, daycare/school, and anyone else that she spends time with are all completely aware of her allergies. Do not allow them to offer her any food (other than things like fresh fruit and veggies) without checking with you first. When my son is at a friend's house, or if a friend is buying food for an upcoming party or event, they will often text me a picture of the ingredient list so I can verify if it works for him or not. Do not feel uncomfortable about asking the host of a party in advance what food will be served - don't expect or ask them to alter things for you, but simply find out so you can bring an appropriate alternative. My son really likes to have the same type of food as everyone else.
Finally, don't let people scare you away from soy. When they're little, soy milk has the best nutrients and is the best alternative to cow's milk - it is most similar in terms of the good fats, vitamins and calcium. It's ok to limit soy somewhat, but to be dairy free and soy free is incredibly difficult. When you're trying to negotiate a dairy-free lifestyle for the first time, the last thing you need is to worry about soy.
I know my post was long, but I sure wish someone had sent me something like this when my son was little! PM me if you have any questions - I am happy to help.