I'm sure this is a common occurence:

My ex wife has custody of the kids on weekends during the school year. This
Weekend she went away without telling me. When I went to drop the kids
Off her sister was there instead. Is this kosher? It would make sense that I
Should be able to have them in this situation. I have no idea what arrangements have been made to care for the kids. The ex does have her mom and sister living in the
Same town, but I still think I should be able to have them.

It's obvious why the ex didn't tell me the plans.

What can I do about this? Do I have any legal grounds? How can I make sure
She will think twice about pulling this stunt in the future?

You would have the kids in that event, I would assume. Her sister has no custody.

If the custody arrangement is for your ex to have them on the weekend - then that it who should have them. If she did not work this out with you prior to you arriving to dop off your kids - then I would not leave them.
You have no arrangement with other family members.

Agreed!

No brainer, don't leave them with anyone but your ex, unless a prior arrangement has been made and you AGREE to it. That simple.

Good luck to you, divorce is hard...

You got to check your divorce agreement and make sure, but as long as you can prove that you tried to drop the kids off with her, and that she alone was not available, you can then use that as proof that she is not available at the appointed time... It may mean involving the police so that there is a record that you tried to follow your end of the agreement, otherwise it may look like you just didn't show up... However, do you really want to put your kids through that? Could it be you are upset that she wasn't there for you to see when you took the kids home. When it is her time. She does have the right to have any person care for the child that she chooses. So do you when it is your time. If you do not want to leave them in the care of the person who meets you, then that is an issue that will have to be resolved. You can choose to go back to court over it, or steadfastly refuse to turn the kids over to anyone but her, but be prepared for repercussions if you try this. The court may find that you are in the wrong and not her, bacause she has made arrangements for the care of the children in her absence. You can choose an adversarial relationship or try to just accept that even though you are right, sometimes it's better for the kids for you to over look what the ex does. Getting screwed by an ex never feels as good as it did before they became an ex, but if you keep what's best for the kids in mind, you will have a good guide for the actions you choose.

You might want to be civil and simply ask her if the kids are important to her at all? If she is at a place in her life where she is not interested in them, then maybe you could make arrangements to get sole custody of them. Children really would like two parents in their lives, but it is much better to have one devoted parent than two, one of whom has no interest in them. Take it from a person of experience.

Thank you all for your input. She did this again recently, but this time I held on to the kids.
Turns out she has been missing for two weeks. No contact, no return messages, no answers from her family. This strange. Where o where is she? In jail, in a mental ward, playing a game with me and planning something?

Let me spell out what I posted in your other thread. Make sure she is not building a nest somewhere else, check if she is still employed, and trust noting she says, and get a good look at her curent b/f. Where he is from, and let your lawyers know, so they can make it illegal to move her kids.

Talaniman, I just read your post. Don't know why I haven't seen it until now.

Anyway, I have put in motion means to keep track of certain people. But she is sneaky and can elude the best. Hopefully she will show up with the kids in the morning.

Let's say hypothetically that she tries to move out with the kids to another state/country. Could she get away with it? How would it be possible to get them back? I've heard of this thing happening. What are the usual outcomes? (if there is such a thing in divorce)

People disappear, and change their names, all the time to get away from exes.

Normally I would say "Okay she ran to the store. At least she didn't leave a teen age neighbor for them to come home to." BUT 2 weeks! And she has done it before.
You should go to court on grounds that she does not have the best interest of the kids when she is taking off for her own wants.
I wouldn't even confront her or anybody about it because if she is sneaky and planning on disappearing that would only trigger her to move faster. Also when sneaky people know you are on to them they just get sneakier.