Two Asian people cooking on a grill in a park.
The couple are cooking in there home kitchen.
You cannot cook in the park and your home kitchen at the same time. (Also, incorrect use of 'there.' Should be 'their.')
Two Asian people do not have to be a couple.  A grill in the park is not located in a home kitchen.
The two people cannot cook both on a grill in a park and in their home kitchen simultaneously.