Kylie -- just as a side note, only one person before you mentioned it at all, and it was as a last resort.
R., there is nothing wrong with playing with your kids! A parent is not only a disciplinarian. But it is important for your ex and you to be on the same page. I agree with the poster that suggested family counseling, it would probably help.
If your children are with you most of the time, your ex should mimic your discipline techniques so that there is consistency with your children. Something that may help is finding your children's buttons and not being afraid to push them. With me, my Mom found out that I couldn't stand upsetting her, so when I spilled red Kool-Aid on our brand new carpet after she told me no drinks in my room, all she had to do was sit down and cry while she was cleaning it up. I can tell you, I never took any drinks in my room again! This technique didn't work with my sister, instead my Mom used "no TV" with her. It's all about the buttons. Your kids have buttons like that, too! Be observant, and it will become very clear.
But the main thing is consistency. Especially between the two of you.
And don't give in to feeling like your ex has the power to choose how you discipline your children. Mom knows best, especially if they're with us all the time. It's because we cherish our children and know them sometimes better than we know ourselves. Your ex can't force you or guilt you into doing something you're uncomfortable doing unless you let him.
Good luck! Dealing with the ex/dad has a lot of struggles, and I think you're doing a great job!