Do you need a full two-bedroom suite (max capacity of 6-8 people) or would a one-bedroom suite with a sofabed (max capacity of 4-5) in the living room be sufficient?

2-bedroom suites are going to be impossible to find as a base award with any category hotel. If you're lucky, they'll be an upgrade award (your existing certificate plus additional points or cash per night), and even then the 2-bedrooms are exceedingly rare.

If a 1-bedroom suite with a sofabed in the living room will work, then hundreds of properties open up to you across multiple brands both city and resort. Some as a base award and some as an upgrade award, but probably a modest cost. I've done MVCI awards in 1-bedroom units with a $50/nt. upgrade charge, and they are usually quite roomy. Comfortable enough for two adults, a teenager, and a 10-year-old.