Is it okay to work in different lab during Summer?
Ask your advisor.

Whether it is okay or not will depend entirely on him. He may have some reason why he wouldn't want you to (rational or not). It shouldn't come across as rude if you ask him openly and express your reasoning (have to go back home but would still like to be research productive and may be a good opportunity to network with the other lab). 

Whether the other lab will let you, is a different question entirely. Another option is working remotely with your current lab.