No you can't use chicken broth in order to cook for a vegetarian. If you go to health food stores or whole foods you can find a variety of vegetable bouillon or even a vegetarian version of chicken bouillon.
These things are easy to find depending where you live. You can also order them online.
It is rather easy to find depending where you live.
My husband's vegetarian, well, pescetarian, and we've been together 5 years. One of the wonderful standbys for upping umame without meat products is Braggs liquid aminos. Low sodium, quite healthy, and a real flavor kick. Also, if you want to go in a cheesy direction for flavor (beyond cheese), nutritional yeast flakes are great. Just use as a flavor enhancer, and watch the salt if you do.
The Bragg's suggestion is awesome, I love that stuff! But it's not a low-sodium product. The serving size referenced on the nutrition facts label is pretty small (1/2 tsp) and shows 160mg sodium per serving. By contrast, Kikkoman soy sauce is 920mg per 1 tbsp serving. It'd take six 1/2 tsp servings of the Bragg's to equal 1 tbsp, and that 1 tbsp serving would be 960mg....more than the soy sauce.
As mentioned before, chicken broth and (most) boullion isn't vegetarian. Even some of the boullions marked vegetable have non-vegetarian bits to them.
Try a few different miso pastes. The flavors vary widely depending on age as well as components. This varies somewhat by brand so try a few within a brand and see how you feel about each one. Other great additions:
*mushrooms, fresh or dried
*caramelized onions (I make large batches and then freeze in small portions to minimize prep times)
*thyme and/or savory, these herbs add a distinct "meatiness"
*nutritional yeast (unappealing name, super appealing flavor)
*tamari sauce (tastes like soy sauce with more flavor and less slat)
You need to sit down with your wife & discuss exactly what she means by being a "vegetarian", because I'm not sure the two of you are on the same page.
Unless the boullion you're using in your sauces is vegetable boullion &/or your wife knows you're using chicken broth in recipes & doesn't mind it, she's either not 100% vegetarian or isn't aware of the ingredients you're using.