Long response but worth the read if you have time...
I am a mom of 2 boys, Quincy almost 5 and Andre 12 weeks. I work 45-50 hours a week. I have a husband who helps me out but he's pulling the same hours as me. I feel your pain and hope I can help at least a little.
This is definitely a very hard time for you, but remember why you are doing it and know that it won't be forever. You are the primary provider for your little girl. You keep a roof over her head, clothes on her back and food in her mouth. She may not understand why mommy isn't always around at the moment but later on in life she will appreciate all you have done for her. Know that you are blessed to have a mom that is there for you and her grand daughter. Does Lanee seem happy and secure when she’s with Grandma? If so there is one less thing to worry and stress about. When you are away from her you are probably depressed most right? At those times try to think of happy times you spend with her or something as simple as her smile. Think about something you two will do when you get together. I know the day gets busy but stop for a minute and just give her a quick call to say I love you. Don't forget Grandma; let her know how much you appreciate all she does. (It won't take longer than a bathroom or a smoke break.) Give Lanee a picture of you two together or your T-shirt that you've worn for about a hour (so it will have your scent)to wear as a night gown.
As far as your anti depressants go... buy a watch with your daughters’ favorite character on it and set the alarm for the times you are supposed to take the medicine. If you can't find the character watch put a picture of your daughter with the pills and set a regular watch.
Three year olds will try to push you to your limits with defiance. They have learned that they are actually their own little person. They are also attention seekers, whether it's good attention or bad attention. How you respond encourages certain behaviors. Don't let your guilt stop you from disciplining your child when she needs it. But don’t forget to praise her when she deserves it.
More than likely when you are with your daughter her energy level is much higher than yours. You also probably think about all the time you think you should be spending together and about how much you are actually apart. Try not to think about that. When you are with her live in the moment. If you're tired, read her a story and have a short nap time. Watch her favorite show with her. Get some crayons and just scribble on paper. Go for a walk at her pace. Take her to the park and let her run wild. Ask her what she wants to do. Try to explain why mommy is away a lot. If she doesn't want to talk about it, it's okay, try later. If she doesn't seem bothered by it don't worry about it. Children are resiliant and you are setting a good example for her. Remember it's not forever. Don't forget to pray (if you believe in God, even if you don't, I do and I'll pray for you). Don't forget to give her big hugs and kisses and tell her you love her. Last but not least don't feel like a terrible parent, know you are a GREAT parent.