How many times can I file an emergency motion for temporary custody?

You should probably follow up on the petition that may be pending. If that case remains pending, you cannot file a new petition, but you can go back to that court and amend your petition. If you are already seeking custody, then you need representation to put forward your best case.

If the original case is pending, do NOT file another case. Have your lawyer (and yes, you need a lawyer - this is not a do it yourself project) determine if the new facts require additional pleadings. If you filed an emergency motion with a scheduled hearing on April 8 and that didn't happen yet, you have likely screwed up, as it doesn't take that long to get some type of hearing, or at least a mediation. If you have an attorney, he needs to explain what happened. If you represented yourself, that probably explains the delay.

If the children are with you right now, then there is no "emergency" to be handled because they are with you, and you are not going to allow the child to bathe with your ex's sister. If your ongoing case is still pending, and you think a hearing is still needed, follow up with your attorney or the judge's case manager and ask for a hearing date. No, the judge does not owe you an explanation as to why the case did not come up for a hearing. Hearing dates change all the time for reasons that usually don't have anything to do with the parties.