Can my mom try to take my daughter if I move into a shelter?

You certainly make a good case as to why you are fit to care for your daughter, regardless of whether or not you were incarcerated in the past. Moving into a shelter as a temporary measure with an active plan to secure adequate housing in 60 days is NOT a good reason to take your child away permanently. If your parents did take you to court, I doubt they'd have a leg to stand on. Provided you have someone appropriate to watch your daughter while you are working and you could show her care wouldn't suffer by being in a shelter for 60 days, no judge should have a problem with it...at least you are looking to better your home life by renting an apartment for your family instead of relying on your parents. You could also possible use it against your parents that they are willing to spend money trying to take your child from you with little grounds when they could be spending it helping you get on your feet. you should go talk to someone at a legal clinic about it, but honestly it doesn't sound like your parents have much to hold against you other than being previously incarcerated, which since it didn't involve your daughter and you have hopefully turned your life around since, shouldn't be too relevant.