Sequoyah Country Club
I don't know about OHTS or The Hills, but I encourage you to also checkout Sequoyah CC in Oakland. There are several levels of membership (we don't play golf and there are membership levels for non-golfers). We have been so impressed with the facilities, the staff, and the number of diverse families with young children at the club. There is a kid's club two-three times per week during dinner and children's swim lessons and juniors golf lessons that those with non-golf memberships can take advantage of. There is a summer camp for children where they play golf, tennis, and swim. There are also a number of family events throughout the year (back to school parties, campouts on the golf course, Halloween and other holiday parties/celebrations.)
Another option to consider is a social membership at Sequoyah Country Club. It is primarily a golf club with two pools (toddler and regular pool) but also a brand new gym and some fitness classes. They are adding more programming to attract younger families. Many don’t realize it’s less expensive to join Sequoyah than the Hills. We enjoy the diversity of Sequoyah, the dining and is pretty laid back for a country club. The Hills has a robust swimming program and the Oakland Hills is better known for its tennis program. We like Sequoyah because it’s relaxing and they have dining, full bar, social activities in addition to the pool and gym.