I am an Ophthalmic Technician and have been involved in the eye care field for over 9 years.
First of all, I have two congratulations -- one to you for not only understanding the importance of your daughter needing to wear glasses at such a young age, but also doing everything you can to make it happen; and the second is to your doctor for explaining it to you (I'm assuming).
I wish I had suggestions for you to help your daughter wear her glasses, but, unfortunately, I don't have any ideas. This was a struggle for just about all parents I worked with. (I have a two-year-old also, so I can just imagine...)
But I want to say that you are right to think she needs to wear them all the time -- that is SO important, especially if she has a "lazy" eye. You may already know this, but because your daughter's eyes have needed glasses, but haven't had them until now, her eyes are used to working hard to try to see (unsuccessfully). When she first wears the glasses, IT WILL BE BLURRY FOR HER, so naturally she won't want to wear them. But once her eyes relax (this could take several weeks) and let the glasses work for her, they should help. If she only wears the glasses intermittently, it will take her eyes longer to relax, or they may not at all. Many children eventually grow out of needing the glasses, but not all.
It is critical for her eyes to be able to see clearly now because her brain is trying to process what she sees, and is, in a sense, "learn" to see. Unfortunately, there is a time limit to this learning. After around 9 years old, the brain can no longer "learn" to see. Glasses won't help with this. For example, if the brain only sees blurry images from her left eye, it may decide not to use it and rely solely on her right eye.
Just one more thought, if she has had the glasses for a while and her eyes have already adjusted, maybe the problem is with the frame. Toddlers are active and it doesn't take much to get a frame out of alignment. It could be uncomfortable. She may need weekly visits to the optical shop to adjust them and keep them in check.
Again, this may be something that you already know. If so, sorry for reiterating it. If not, I hope it made sense. It's just that I've seen so many children whose parents haven't follow the doctor's instructions and then it's too late. So bottom line, you are doing the right thing -- stay with it!