@YogaLite just understand that nobody has rights to information about you. Only a few people like government agencies, the bank, your employer etc has a right to certain information. Everyone else only has a right to what you're willing to share.
In life, people want easy situations, we're all busy and stressed and times feel hard, even though compared to history we've got it easy. People want simplicity, convenience and fun. So if you want friends, that's what you have to be.
Basically, don't open your heart to people because majority of them won't care. Most people are mainly selfish and won't waste their precious downtime and energy on other's misery. So yes, to an extent you have to keep it hidden. Everyone is fake to some or other extent. How fake you are depends on how much shit you have to hide. Just look at social media. Edited positive highlights of people's lives. Not reality. It isn't much different in person. The only socially acceptable answer to "how are you?" is "I'm fine, thanks".
No need to deny your DC existence, but understand that nobody cares what your life is like or wants to know how you/they are. Not even if they insist they do. People can't deal with it and will essentially mentally run away and physically avoid you in future, no matter how caring they seem at the time or how much they say they don't mind listening or that whatever it is doesn't bother them. Those are self serving polite lies, both to spare your feelings and to avoid them looking selfish.
I agree with Olive, change the subject. Speak of the positive and not the negative. If pushed, extricate yourself from the conversation and avoid the pushy ones in future. They're being rude! You have enough to deal with without that. Their desire for gossip doesn't override your desire for privacy. They can fuck off. As you've found out, they'd only take the information and use it for gossip, or it goes in one ear and out the other as they quickly dismiss you as someone who can't add anything to their life. They have no intention of befriending you or being kind, they're too busy doing what suits them, and that doesn't include having to make allowances for disabled people and their carers. You owe them nothing.
There's an ancient quote about being stoical and getting on with life.
"Many men live lives of quiet desperation and go to their graves with their song unsung".
Those who you may envy for their better situation may actually be no better off than you are in life, just for different reasons.
Keep conversation light and fluffy, refuse to have your misery used for others entertainment. You can mention your DC is disabled and goes to a special school and is doing really well there, without mentioning the 3yr legal battle you had to get them a place and how disgraceful it is. You can mention being unable to meet up at the park and offer instead a multipack of ice lollies and an inflatable paddling pool in your back garden for a playdate, without mentioning how you can't ever go out due to your DC unpredictable behaviour.
Before you answer something ask yourself if it will help you for the person asking to know? If it doesn't, brush off the question.
Sure, it means people will end up thinking you're doing better than you are, but what happens if they know the truth? Do they come rushing to help, to ease your load in some small way? Do they heck. They leg it in the other direction!