Your family has a few options. The closest one is General Sams located just north of Huntsville. Most of the trails are on relatively flat ground with just a few trails that go up/down a hill or ditch. If you stick to the permeter trails, you should have no problems with newbie riders.
In my opinion, a better place for newbies is Rural Shade ATV ranch located not far from Corsicana, TX (on I-45). This is about a 2 hour drive from Conroe and its VERY FLAT. I took my 2 kids there last summer when they were new to ATVs and they had no problems at all. Most of the place is open pasture with a few wooded trails here and there. Also, I've always found the customers to be friendly (not wild party animals like you often find at other parks like Shiloh Ridge).
Another option is Mud Buddys. I like this place b/c it has a nice variety (wooded trails, sand drag strip, MX track) and the family that owns it are very nice. However, its is a bit on the smaller side (200 or 300 acres), so its probably best for a day trip (might get bored riding here for 2 or 3 days in a row). Its about a 3 hour drive from Conroe.
You could also find lots of safe, flat trails at Mud Creek in Jacksonville, TX and also at Soggy Bottom near College Station, TX. There are other atv parks within a 3 hour drive of Conroe area, but they are more techical (like Shiloh Ridge in Alto, TX and River Run in Jacksonville, TX).
Happy trails...:)