East,
I know I harp on this, but I harp on this for a reason. Why the heck is your daughter having a daily phone calls to her mom before school?! The morning routine is stressful enough for a kid, but to fit in an obligatory phone call so your ex gets what she wants is by far too much pressure on a 6 month old. Obligatory and timed phone calls multiple times a day put stress on a kid. They are just trying to manage school and friends and be a kid. Do you have obligatory times calls with her too? They are obviously as stressful thing for all involved. Who are these calls for? You or your D? If you are away one or two nights, there is no need to have them. Trust me, she won't forget you. She will still know you love her.

Your child can feel the stress in these calls. How about when SHE says "hey, can I call Mommy?" then you call her. If she says at her mom's, "hey, can I call Daddy?" then she calls you. They don't need to be full on question and answer sessions on facetime. Maybe both of you can just shoot a call that doesn't even involve questions about her day, ect. Just a hi, I love, you and goodbye. Don't lead the convo. Let the child lead the convo.

I know all of this from raising my daughter in such a situation since before she could talk. I've been through every stage up until 10 (where we are now) and her own phone is a beautiful thing! Taking to psychologist, I had them help me guide me on what is best for her . Not me, or her dad, but HER. And they all agreed at 6, their interest to talk on the phone is limited to less than a minute. They all agreed they should be focusing on time on the parent they are with. Her calls with her parents involve interference and tension and the poor kid doesn't even get to talk. That is extremely stressful for her. So, eliminate the stress. She will see you and talk one on one with you when she gets home.

I do hope you start some therapy for your D. It would be a great outlet for her. Especially when she needs to learn how to deal with the new news. Just a 3rd party where there is no bias, and she can speak about her feelings where she isn't afraid of hurting anyones feelings.

As far as support, you have it, even if it's not physically there. I never had my support physically present for my big moments, I've been single for the much greater part of the last 10 years, I am an only child and my mother is dead, but I have a great father. I talk to my friends. They are there for me.

Do you have friends, east? Family? Even if they can't be physically there, you do have support. Lean on it.