My 2.5 year old only tells me that she has to use the restroom when we go out and do errands or stay at another family members house to visit. When we are at home she will just pee wherever and whenever without telling me. She only tells me after she has already used the restroom. She enjoys the cleaning up process and still tries to play with the pee puddle occasionally. I do not know what to do in this situation.
Your 2.5 year old feels safe at home, and so is happy to test her boundaries and learn about things at home. On the road, at Grandma's, etc., these are less familiar environments, and she'll naturally act more restrained, take her cues from you as to how to act.
How you deal with it at home? Well, congratulations, your daughter knows how to tell when she needs to go! That's the hardest part of potty training. Everything from here is just teaching her to choose to do it the polite way - i.e., in a toilet. The standard way to deal with this is either treats/potty training chart, I'd say; you don't really need the "naked weekend" since that's more for learning how to tell when you need to go rather than behavior modification.
She's getting a lot out of the attention when she fails to go properly, so just turn that around - give her lots of positive attention, and something she likes, when she goes properly. Stickers, a single small candy (like an M&M worked well for us), or a chart where she marks off (with a sticker or an X) when she successfully does it, and gets a small prize when she finishes a certain number - we had small prizes for every 10 (like a car) and larger prize for a week without accidents.
If she won't regulate herself, for whatever reason, you have to do it for her. Don't wait for her to say anything, don't ask her if she has to go; tell her to go. "Lunch time, but first we tinkle". "Let's tinkle before we get dressed". Say it like it's a thing that is going to happen, not a suggestion up for negotiation, or a question to which 'no' is a viable answer. She's only 2 and a half, it's okay that she she needs some guidance.
Get her body in the habit of only tinkling in the toilet, and she'll stop wanting to go anywhere else.