I was thinking about our experience of babysitters. 2 that we had asked if they could bring their boyfriends round, and we were happy with that. In fact one of the boyfriends ended up babysitting the DC for a couple of days each week during the summer and he was a real hit. Not that I would necessarily endorse a blanket yet policy to friends / boyfriends accompanying the babysitter, but we had had a chance to meet them and were happy with it. We have also had lots of babysitters who bring friends with them.
If anything, I think the driving to another park would bother me more, but I can't really articulate why - perhaps because I wouldn't know their standard of driving etc. Walking to the local park wouldn't be a concern for me.
When we had a nanny I was happy for her to bring DC out and about on trips, but it just feels slightly different for a babysitter. At the end of the day though OP knows her circumstances best, knows the babysitter and her level of responsibility, and presumably has a feel for the boyfriend.
Re-reading the OP, one of the things that stands out is that even when your DH said he wasn't happy with her bringing kids to the further park, she wouldn't take no for an answer, and was focusing on meeting her family. There's being flexible, but that would jar with me.
I'm not sure about the fixation about how much OP pays. I agree with her, no matter what she says, some posters will pile on and say it's too much / too little.
OP I think you need to start putting feelers out to see if you can find anyone else. Always good to have a back up anyway. Do you know any teacher friends? I've always found that a good way of finding responsible late teenagers for babysitting.