I am not divorced but I do understand your situation. One of my closest friends is going thru almost the very same thing, except her ex always had good phone contact with his kids.
They have their landline and cell phones, her and DH, plus both kids 15 and 11 each have their own. They set the kids up with their own personel e-mail accounts as well. The EX use to work 3rd shift and for years (a little over 5 years), he would get up around 8:30 in the evening and call the kids before getting ready to leave for work and them going to bed. Even on the weekends he didn't have them, they kept the same call time. She would call the kids at this time, when he would have them for his visitation.
Fastforward to six months ago. He changes jobs and is now on first shift. Both kids are active in sports during the summer as well as the school year and the 15 year old works at their church's nursery/day care center after school and during the summer months. As soon as his hours changed, he started calling them when he left work, 4 p.m.. If neither of the kids answers their cells or the home phone, he is calling her at work...where are the kids, they didn't answer my calls. If he gets her voicemail at work, he called her cell. If still getting VM, he'd call her DH's cell number. If he didn't get a hold of any one by the time he got home, he would start sending e-mail messages to all of them, including her e-mail at work, as well as continuing to call all their numbers. There would be times that he was calling from his landline, texting, and sending an e-mail all at the same time, with the same demand - WHERE ARE YOU AND WHY ISN'T SOMEONE RESPONDING TO HIM.
She has told him, call and if no one answers, leave a message and someone will get back to you as soon as they can. Calling or e-mailing every five minutes doesn't get you a return call any quicker, because we don't always have immediate access to the phones or e-mails. The 15yr old can't have her cell phone on her at the daycare center. The 11yr old can't have his cell phone on him at ball practice.
The worst case was when her grandmother passed away. He was told that she had passed and that they would be at the funeral home Thursday night, all day Friday, and busy with the actual burial and services on Saturday. Told him the kids and DH would not have their cells on them, but she would have hers in her purse, turned on but with the ringer off. If he needed to reach them, just leave them a short message and they would get back to him when they could. He showed up Thursday for the funeral and was nice as nice could be. Friday night when she checked her cell, from 4 o'clock on, he had call every 15 minutes until 9 o'clock, she got the messages around 9:30. As a family, they had gone to get something to eat and she just never checked her phone, when they left the funeral home. They called him as soon as they saw he called. He was out and couldn't talk, said he'd call them the next day. The 15yr old reminded him that they would be out all day and that they would be leaving the house around 8 in the morning and that she or her brother would call in the morning before they left. Told her not to call, as that would be to early. Around noon, the calls started. And not just to her cell, but her DH's and the kids cells, as well as the home phone. Plus, text messages and e-mails. Around 2, my friends neice came up to her and told her that something in her purse would beep every once in awhile. She went and checked and she has 20+ messages from him. She gave the 15yr old the phone to call her dad. According to him, he just wanted to make sure the kids were doing ok. When they finally got home, they had over 30 messages on the landline and 30 e-mails - where are you and are you doing ok. She was beyond seeing red. The kids called their dad, and he was getting ready to go out, so he didn't have time to talk, he'd call them the next day. Any guess as to when he called......around 10:30, while they were in church.
The kids have ASKED him to go back to calling at 8:30 like he use to, that they had always looked forward to this time. But now that he's working normal hours, that doesn't work for him. He's not always home at that time, he needs to be able to get in touch with them at his convience. As the 15yr old him, well dad I don't know what to tell ya, because when it's a convience for YOU, it's not for me or her brother. Sorry we have to fit into your convience to talk to you. And it's not gotten any better. They have been saving every e-mail, they get detailed cell phone bills and they keep a log of the landline calls.
So I do understand your fustrations. Like my friend has stated, I'm glad he wants to be in touch, but this is over kill. And they kids are getting to a point where they could careless if they talk to their dad.