作为建议,提议的意思,其用法有:后接[+v-ing] [+(that)] [+wh-]
I suggest our going to the park on Sunday.
我建议我们星期天去公园.
The dentist suggested that she (should) come another day.
牙医建议她改天再来.
你说的用法也可以见到,比如第一个例句,就可以改为:
I suggest us going to the park on Sunday.
但us不是suggest的宾语,而是going的逻辑主语