How close is too close?

I know I'm so cool people can't help but feel drawn to me. Totally joking!

But I have a serious question. How close is to close when you work for somebody? I technically work for myself but I get paid to watch peeps kids, I guess that means I work for them because If I didn't watch those kids I wouldn't get paid....duh!

Well one of the girls I work for is really pushing friendship, and at first I thought it was all cool and good and possibly we could be friends. I'm starting to think she's pushing friendship to try and take advantage of me. She's always trying to get out of paying me full price, which I freaking HATE.
My reasons would be I don't charge that much to begin with and I work my ass off to keep the kids clean, feed, happy and learning.

Now what? What do I do?

The other 2 couples I babysit for want friendship too, the only difference is I TRUST them, they never complain about the pay or ask how much they owe they just know what to pay, they don't try to get me to babysit Saturdays or holidays.
One of the couples even has given me more then what I ask on more then one occasion (for supplies or just because they know I work hard). I so love them by the way they are two of the coolest people I have ever met.

Even with all that said How close is too close?
I want to keep it professional, I want them to know I like them and I love there kids. How do I do this and what do I do?

Is it okay to go to birthday party's or out for ice cream and so on, or is that not okay. Is going out without the kids okay or is that a total NO?
I'm so lost. HELP!