Well, it isn't poison ivy or poison oak. If you were here in NJ I'd say they were mulberry seedlings, but I'm not familiar enough with Texas plants say that's what it really is. There are other plants that can cause problems in people that are sensitive to them, maybe your wife is just unlucky (or lucky, since you're now the one doing the weeding.) Poison ivy always has leaves with 3 parts; poison oak is similar but the leaves are more rounded; we don't have it up here in the northeast, don't know if you'd have it in Texas. Poison ivy is pretty variable, but what is in your picture is not it. Your bushes are azaleas. WW Here is a link that might be useful: This IS poison ivy

Looks like privet.

The proper method of rejuvenating woody shrubs is to cut them ALL the way back to the ground and force them to produce a flush of juvenile growth. Many shrubs will not produce much attractive juvenile growth on old wood, even after a pruning, and will remain stumpy and gawky looking. Rejuvenation pruning solves that issue. Rejuvenation pruning is best done in early spring, just as the plant is beginning to come out of winter rest. Cut the plants, neatly and cleanly, to 6 inch stumps or less. Recovery will be rapid. Do not fertilize. Many species respond beautifully to this, but there are exceptions. I'm afraid that you have not given us much to go by regarding an identification. Are the leaves opposite on the stems or alternatate, for starters? (pinnate not much of a clue) Evergreen or deciduous? Any other notable characteristic, like flowers or berries?

Picture is pretty far to be sure but leucadendron safari sunset is my guess.