This must be something more than just social anxiety because if you can't go into your own garden when there's no one in it that you have to speak to, there must be more anxiety going on than just interacting with people
A lot of social anxiety is about being looked at. It's not just about talking to or otherwise interacting with people. I have SA and I run, but It took me years to work up to being able to do it, and usually I have to wait until after dark.
I still struggle terribly with making and keeping friends.
OP, numerous antidepressants did nothing for me. The only thing that did was a benzodiazepine, which is the same class of drugs as diazepam.
Some things (the smaller ones) really do get less difficult the more you do them. Doing nothing makes it all worse.
And yes, your children will pick up on the fact that you are scared of the world. And growing up in a house that no one visits, with no family friends, or where they feel they can't bring their friends, is probably already having an effect on them.
Your DH probably thinks he's helping you by dealing with all the things you find hard, but actually he's enabling, not helping.
I agree with the poster who suggested you make a list of things in order of scariness and start with the least scary ones. As well as drugs and talk therapy.