If you want to avoid Houston your best bet is to go through Winnie and take the ferry across to Galveston. As to a stop along the way the KOA in Onalaska on the shore of Lake Livingston is nice, they have some pullthrough sites where you should be able to fit without unhooking. About the only other place we have stayed with pullthrough sites in the area is Home on the Range RV park a bit north of Huntsville on I-45, it is cheaper, and has a fairly good cafe on site (Shrimpy's), though sites are gravel, not as level, and a bit ran down with a number of long term residents.
2002 Safari Trek 2830 on P32 Chassis with 8.1L w/ 400 watts solar 420Ah LiFePo4
2017 Jeep Cherokee Overland & 2007 Toyota Yaris TOADs with Even Brake,
Demco Commander tow bar and Blue Ox / Roadmaster base plates