I am personally against leaving a child in a crib to "cry it out". I feel it affects their trust issues. Even at 1, they have security issues. I have a feeling these tantrums are like the previous answer is, she doesn't seem to want 2 naps. Does she have a regular routine? Getting her up same time every day, getting dressed, then eating breakfast...and so on. When it's time, it's time for things. Children need routine, and family to stick to it. Right now her world is a little upside down because dad is gone. She's trying to express her feelings. Was dad a stay at home/work from home dad? Did he put her down in the afternoons? Try putting a rocking chair in her room, rock with her....darken her room with dark curtains, and about an hour before you plan on a nap, choose some quieter activities. Maybe reading to her, give her some milk with lunch...ect... And remaining calm yourself helps. My son really reacted to the "shhhh"-ing technique....where I patted his back and just did "shhhhh" next to his ear....and swayed with him. Still works today when he gets upset. He's 2 now. Does your daughter have a "lovey" or object of security? Maybe even a pacifier? Something that she associates with comfort. Maybe even laying down with her in your bed, and show her how to take naps....
Its hard to say...but I have a feeling that she's feeling dad's absence and is trying to tell you that she's upset...her "people" aren't all present. I always tell my son when I have to go away, I tell him I'm going to work. He understands that with "work" we always come back.
Good luck, and don't be afraid to try different things.
If she goes to bed at the same time every night, does she sleep all night? Does she have a set bedtime routine? For example, if she gets up at 8-8:30 in am, then a nap around 1-1:30 is ideal. If she does sleep, don't let her sleep longer than an hour and half. Even if she's still sleeping when you go in to get her....then get ready for bed around 7...start to keep the house darker, go around and close shades, turn on lights, but low...keep TV noise turned down low....have her help pick up toys and indicate this is part of getting ready for bed. I've always given my son a bath/shower every night. I use the lavender scented bathtime soap...either J & J, or store brand...all the same. He gets scrubbed down (shampoo is at a different time, usually mornings), then can play in water for a little. Then we brush teeth, get rubbed down with nightime lotion (same scent, trust me, it works wonders!!), jammies on, read 1-3 stories, then it's time for one of us to rock a little with him, with light out....he tells us ready for bed....and we put him down in crib (he hasn't shown any attempt to climb out), and within 10-15 minutes, he's asleep!
I hope this helps you!!
Good luck!
Just remember, Rome wasn't built in a day, so don't expect her to change immediately either. It's going to take a little, but YOU need to remain consistant. It will work out in the end.