Four months old is so young! Now granted, by the time I had my fourth, I was out and about for a half hour or an hour at least once a week sans baby by that point, but she was left to a house full of doting brothers and a daddy who wouldn't put her down
But with my first two, I was like you, I felt totally naked without them, I didn't even like to let them nap alone lol! I think, though, you should let your dp take them out for a walk every day, just 20 minutes or a half hour. It's good for you to get a little break like that (this is the mother in me talking), and good for her to be "in charge," as it were (this is the wife in me talking). She's proud of her family just like you are, and OF COURSE you can go with her, but maybe she would like the time alone with the boys, too? Maybe not, just something to think about. What you are feeling is totally normal and shows you are truly bonding with your babies. It's nothing to be ashamed of, just don't lose your "self" in it.
And don't listen to anyone who tells you otherwise, you are the only one who can assess their needs like that (of course your dp can, too, but she's not pressuring you, so it's not an issue, kwim?)
congrats on your bundles of joy, sounds like you have a very sweet family