As you have said, your child can’t help being who he is. If there is a reason behind his behaviour/personality then only you can do something about this right now and that’s get him tested for behavioural issues.
Do you think he understands how you feel? Children are not stupid and they know how their parents really feel about them.
As an outsider who is not in your position i can only speculate on what I would do. I’d firstly look into testing ASAP. I’d also start looking at ways to change yours and your DHs behaviour with him. Sitting him down, talking about boundaries and behaviours for a start. I’d stop prioritising his needs over your DDs too.
Maybe start doing things separately as a family, your DS and DH have days out together doing things DS loves, look at the big inflatable courses that are popular these days, have him burn of energy, go ape courses, something he can be loud of extroverted on, go karts... Something that he can be himself on. You may be lucky and DH may start to bond with him in these activities.
While they are doing that you and your DD can focus on something just for her. Then the following month, it’s Mummy Son day and DH has a Daddy daughter day... if these are put into the calendar, he can spend time and energy planning things he’d like to do with you both.
When you do things as a whole family, do things where you can take time out, if say at a theme park and DS is getting too much for one of you, just say, hey why don’t me & you go do this together while dad and your sister go get us some drinks, then dad takes dd off to do something and you meet up after a short pause from each other. Rotate it through the day. I can’t remember the last time we spent the whole day together at a theme park, I usually take the little one off while DH dose the rides with the big 2 then we swap for anything with heights as DH dosnt like them. We meet up at certain times throughout the day, for lunch, drinks or watch shows etc.
I would totally avoid situations you know is going to cause discomfort to everyone quiet places, restaurants etc... anything with restrictions why put you all through that when you know it won’t end well.
Maybe look at some activities where he can also be himself, drama, he can definitely be the centre of attention there and there will be others just like him. One of my DDs would go for 3 hours on a Saturday before covid, something like that would give you all some respite. Or if he’s physical then maybe boxing or kick boxing, in a gym where they will teach him discipline. Maybe set up something at home if you have room.
My DH and I have always done one on one time with each of our DCs, including weekends away, they choose, what they want to do and who with. This way they all get individual time with us.
One thing I’d immediately put a stop to is other people comments and opinions. This is your child, you need to have his back and be 100% on his side.
Other children tell me he irritates them.
My response would be, I’m sure some people think your irritating at times too! If they get upset, tough.
Friends and family comment to me about his unusual personality.
my response, I know it’s fantastic isn’t it, not sure who he takes after! Or What do you mean unusual? What are you saying about my son, there is nothing bloody unusual about him!
Teachers always commenting how he never shuts up.
ask them if they want you to gag him? Ask them if they are qualified teachers as surely as teachers they should be use to all sorts of different personalities.
I worry what his adult life will be like. it will be happy if he feels happy and loved.
There is a mum I know through my DCs school, your situations are almost mirrored, DS & DD the same age as yours. Her DS actually got expelled from school though. She said it was the best thing to happen to her son as it meant he was able to get into another school that was better to cater for his needs. I know they do a lot of outdoor activities where he can burn energy off. He loves animals so they focus a lot of time where he can spend time with animals too. But their dd still gets to go her things too.