I'll say a few more things and then shut up, but I don't know what other members will make of it, which is: sometimes a good attitude can heal an insecure person. (this is my experience, your situation may be different but hey, worth a try, if you already didn't do so).
In my first marriage I was a kind of wife you describe: insecure, jealous and neurotic. My 1st husband's attitudes/actions didn't help although I never texted him every 30min or tracked him. But I snooped on his emails or texts, feeling like a total shit, and what I found only made me feel worse. When he left me saying "You need a carer, not a husband" I, thankfully, didn't buy it but I was thinking I'm so vulnerable no other man would want to be with me.
Surprisingly, it was't true. My following boyfriend's occasional phrase "You just don't flirt with anyone if you're attached", as well as avoiding a particularly flirty female friend who was a hit with men, made me trust him to the point that I was good friends with his ex who was very much on the scene. She and I met for lunch/drink, and we three went out together to a film or meal, all very civilised and friendly without any flirty bs. On one occasion he gently kissed her hair in my presence and I was deeply hurt but gave myself 2-3 days to see how I feel about it before saying anything. In the end I didn't, and dropped it altogether. He was just a very gentle caring person.
My second husband absolutely adores me, and I'm the one who gives reassurance - because I know exactly what to say, i.e. what I wanted my 1st Husband to say which he didn't. I can give him all my passwords, he can read anything I write to others, because whatever I say about him is that I can't believe I can be loved that much. So, the bottom line is: you can help your wife to feel more secure in your marriage.
You said you love her. If this isn't a half, then it's 2/3 of what a good husband is. Then tell her you love her, send a text. Or buy flowers. I bet she won't bark at you "what's that for? are you guilty of something or what?" I bet she will be genuinely touched. Try to spend time with her away from the kids, if you can afford a childminder. Make her feel she - and the children, your family - are the most important people in your life. Stay with the kids so she can go out to see friends. If you email anyone, make sure you don't say anything about her she'll be upset about if she reads it, for she probably will. You say she doesn't like your friends. Is it because she is never there when you see them? Are there any people who are "harmless", another couple, you can see together? And show to them, by gentle touch or smile to her, how much you value her, so she doesn't see social interaction as a threat? For a vulnerable, jealous person it's important when a partner shows OTHER PEOPLE how much they are loved.
What I'm saying is the men I met after my 1st husband, their attitude and actions, turned me from an insecure downer of a woman into somebody jolly, friendly, supportive and not jealous at all. I even gave up antidepressants I was taking for 20 years.
I hope this helps, and by all means good luck. It might be a shitty time in your life, but you may overcome it, and still be together in old age, looking after each other.
Love to you both.