Research Experience in Summer (With POI?)

[miffle]

I have several questions about getting more research experience in the summer, and whether it's strategic or not strategic to try and work at the labs you plan on applying to for PhD.
I am in a social science masters program at the moment, and want to stay as productive as possible during the summer before PhD application season. Along with working on my masters/thesis projects, I was thinking it might be a good idea to do some research in another lab to increase research experience, as well as do some networking. However, I have a few issues that I'm not sure about:

1. I might want to do summer research in labs I'm potentially interested in applying to for PhD. However, my masters gpa is not so hot right now (I'm planning on fixing it this semester). Would it be a bad idea to get in touch with these labs, given that they will want my CV and gpa looks weak right now?
2. Is it possible for me to ask to do research remotely for summer if I apply to be a temporary RA in someone's lab? Or would this come off weird? I usually assume I won't get paid to help with research, so I'm not sure how feasible it would be for me to travel to the lab. The easy answer to this is to just only apply to labs that I can physically get to, but (1) I'm not sure yet where I will be during summer (I may go home or stay where my masters program is), and (2) the labs I'm interested in aren't always physically near me

Hopefully this is a useful question to other people. All input or suggestions related to summer research are deeply appreciated!