Technically, one only divides herbaceous perennials, not woody plants. However there are some exceptions. Hydrangea macrophylla is a caning shrub or one that generates individual stem growth ('canes') from the root crown. Caning shrubs lend themselves better to any sort of division than do other types of woody plants but the process is not foolproof and results are never guaranteed!

You really should dig up the entire rootball and gently separate the two major portions. Don't just jam a shovel in between the two - it could damage both. And wait until late summer or early fall just as the plant starts to shut down for the season before attempting.

In your opinion, would separating them like you suggested endanger the entire rootball and I should leave well enough alone? Or will it do better if I separate them?

I don't need another one anywhere (although I can easily find a place for it), so my main goal is to make this one healthier and look better.

I think the biggest risk is to the smaller portion. But I personally would not do so intentionally unless I were lifting and moving the entire plant. Wait until the end of season, see how it looks and make your decision then.