When DD1 was diagnosed, over 8 years ago now, my overwhelming feeling was one of relief (and slight vindication - I'd had 2 years of battling with the doctors trying to get them to acknowledge that there was something wrong), primarily arising from the fact that DD1 had been so ill, I'd thought there was something really seriously wrong with her, so to find out that all I had to do to make her well again was to change her diet was a big relief.
It does make life difficult, there's no getting away from it. But awareness and understanding has increased dramatically, just in the time since DD1 was diagnosed, and the supermarket shelves are now stacked with free from foods, and the labelling is clear. My DDs (all three are coeliac) have had to have packed lunches at school, but DD1 is now at secondary school and they are much better set up to deal with gluten free as all the food is made fresh.
You identified the one area which was most upsetting for my DDs when they were younger - going to a birthday party and not being able to have the cake. I always used to ask the mum hosting the party what kind of food they were supplying and try to duplicate it as much as possible, so they didn't feel too different at the actual tea (although sometimes their friends would like the look of their g-f food, rather than the party food!), but the cake is a tricky area. I have a couple of friends who bake their own cakes and were happy to bake gluten free and you can now buy gluten free birthday cakes in Marks and Spencer so it is much easier to cater for coeliac children.
Just as an aside, M&S do a great range of g-f food - pretty much all their sausages are g-f, they even do ready cooked cocktail sausages. They have g-f scotch eggs as well! And (as the festive season is on its way), their Christmas range of things like stuffing, pigs in blankets and sausage meat is mostly gluten free too - my whole Christmas dinner is gluten free and no one notices any different.
If you're a baker, substituting Doves Farm gluten free flour for standard flour in most recipes works very well - just add a little more liquid as it's much more absorbent. And you can make an amazing white/cheese sauce with Doves Farm rice flour - the recipe is on the pack.
I hope some of the above is useful - it's a tough time, but once you've moved onto the g-f diet, I'm sure that the change you'll see in your DD will make it worthwhile. My DD1 was a changed child within 2 weeks - she'd always struggled to eat and had no energy and watching her shovel in gluten free pasta with gusto used to make me very teary in the early days. Best of luck - happy to help with more information if you need anything 
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