I don't think you've ever got the right to tell someone how to make organise their family life or child-rearing, but you do have the right to tell them what you want when it comes to them being with you.
So if they want to take their kids out in a vest and pants on a winter's day, you might not be able to say they shouldn't, but you do have the right to tell them that you won't take them out without coats, warm clothes and hats, for example, and that they must be provided.
That's quite an easy one, but a more difficult one is if they swear in front of the kids, so the kids swear in front of your kids, which may not be what you want in your home. Again, you don't have the right to tell them not to swear in front of their kids, but you do have the right to expect your children not to be exposed to that. So I'd suggest you have the right to discuss it with them! And if you can't come to a compromise you're both happy with, you have to part company, as ssd suggests.
That's just examples, but I think its true of anything - if you can't agree on issues which to both of you are really quite fundamental, then neither of you are going to be happy. I went to see a childminder recently who had the TV on all the time. Lots of people would feel they could compromise about that. I didn't. That's my bottom line. On the other hand, the childminder I've chosen doesn't cook proper lunches, just has sandwiches or beans on toast. I find that perfectly acceptable, lots of people wouldn't. It's really what both parties are happy with.