If you don't have sensory issues, you have NO idea how absolutely crippling they can be. I honestly think at some point they should be considered a disability if you have them severely. They can be THAT bad.
As a kid if I had to wear something that itched I literally couldn't learn, think or cope with anything. Where others would say they 'got used to it' and then it stopped bothering them, for me it got worse and worse, like someone hitting the same thumb over and over with a hammer. I went to a school where NO ONE understood sensory issues and it could be severely overwhelming and scary. And it wasn't just itching, LOTS of things set off my senses. I was truly blessed because my mother grew up being dressed by her great aunts after her mom died. Back in the sixties that meant her clothes were totally out of style until she learned to sew them herself and every single of those outfits itched. So she swore her kids would not ever have to wear itchy clothes. For me that was a lifesaver. She even sewed my school uniform instead of buying it because the seams were sewn with a special heavy duty thread that itched and poked you on the store bought ones.
It really is easier to tell people some sort of standard excuse like "I don't want to" or "I have a headache/cold/whatever" rather than to explain that the noise or taste or lights or smells are so bad for you that you cannot cope.
PLEASE, PLEASE PLEASE PLEASE, look into ways to understand the sensory issues your kids are coping with. Your son may be able to have brushing therapy which actually can reprogram the brain to cope with sensory input so that the sensory issues are greatly relieved. It MUST be taught by an occupational therapist because if you do it incorrectly you can really mess things up. For example brushing the belly can create great stomach upset, so you have to avoid that. THe brushing is done with a surgical scrub brush and can be done either over or under clothing depending on what the child likes andthe situation (you wouldn't brush under clothing in public, for example). It is easy but must be done often. Using this therapy my thank you went from missing at least 1/4 of every school week due to sensory overload (he would just sit and shake and shake for hours if I sent him to school when he was overloaded. It could take up to 2 full days for it to stop, and he sort of just shut down totally at those times, which was truly scary for hubby and I.) to having near perfect attendance in just about 2 years. After about 6 months he stopped shutting down when he was overloaded.
OTs won't do brushing on older kids because they say it won't work. I beg to differ. I was taught it for thank you and then wanted to see hwat it would do for the other kids. After a month of just doing it once or maybe twice a day, even Wiz could see a HUGE change in how he felt when he was overloaded and he didn't get overloaded as often. I also did it to myself and the changes in what I could handle were astounding. I even wore a dress to a function that had one spot where it itched and I was able to ignore it, which for me is HUGE! Considering that the Occupational Therapist (OT) told me it wouldn't help me, I found that interesting. I did not expect it to work because it seemed to me that just brushing your body and expecting your senses to work more normally seemed like hocus pocus more than actual treatment, but I gave it a try on myself because I wanted to know what thank you was going through. I didn't brush the older kids until several months after I saw what it was doing for myself. I think the conventional wisdom about the brain not being able to be helped with this (which is what our Occupational Therapist (OT) told me) is wrong. I think our brains are far more able to change than we know, and it doesn't stop at a certain age. That is just my own belief though.
I am not saying that you should do this on you older child, or anyone that isn't seeing an Occupational Therapist (OT) for this. I am just telling you what I did and what I experienced.
Please be aware that your kids may not be ABLE to tell you that this or that sensation makes them uncomfortable or upset. My thank you still, at age 15, has a tough time telling us what is wrong when he is sick. He has to really stop and concentrate to tell us where the problem is and to describe how it feels (sore, hot, achy, etc..). His sensory issues make it really tough for him to figure out what is wrong. He just knows something is wrong and he is overwhelmed by the feeling to the point that it takes reading his actions and body language to figure it out. In some ways it was sort of like having an infant again each time he got sick because I had to find and help the problem without him telling me that his head hurt or his stomach ached or whatever. So your older child may not be able to tell you why being with everyone is too much. She just knows it is and that she cannot cope well, so you have to help her figure out if it is the noise, having so many people around, the scents, or whatever the problems are. that is tough with a teen, and may take some time.
I strongly suggest reading "The Out of Sync Child" by Kranowitz to get more of an understanding of sensory issues. For your younger son, "The Out of Sync Child Has Fun" by Kranowitz has activities to help provide the sensory activities that will help him, along with many ideas to make it less expensive to do those ideas. The activities really are fun, and my entire family and all my kids' friends loved many of them. We wore out at least 2 copies of that title just enjoying the different activities. The key to really getting the most out of the book is to let the kids drive which activities you do. If they really don't like an activity, then it provides a type of sensory stimuli that bothers them and you should not push them to do the activity.
I hope this helps. Sometimes having a better idea of what is going on can really help you tolerate a Difficult Child. At least it helped me.