S.R.
There is more going on here than your job, I bet, as you say she never really slept well for you before this started. The first thing I would suggest is spending time with your parents on what exactly they do before and during putting her to sleep. Nowadays we take so much for granted-- loud music, ingestion of sweets/caffeine, etc. Take a look at your own life-- are you doing things that rev up your child before bed? Compare what your parents do.
The second is a take-off from your change in routine, ie from non-working to working schedules. As you note, this can be disruptive. Is your husband handling putting her to bed in your absence? If so, does he do this when you are around, too? If not, that might help so that your daughter doesn't associate his presence with your absence. Also, you might see if he has problems putting her down.
Also, how can you both work together to create a routine for this child? Even in your absence, there should be a definite structure to her day-- create a definite routine for going to bed and be consistent in following it. Perhaps one does some quiet activities-- having a bedtime snack/bottle, soothing music, reading a story, taking a warm bath, whatever is best for her and your family. Take her upstairs at a set time, which seems to work for her. Maybe spend some time reviewing the day and planning the next. Tell her she and you all need a good night's sleep in order to do all these nice things. Let her know your plan-- if you cry, we will come in to check on you, but if there is nothing wrong we will close the door and leave you until morning. (If that's your plan.) If she continues to cry for your husband, maybe you can take the 3 year old with you to babysitting so he can get some sleep? Would it help to arrange with her that you will come in when you get home from babysitting to say goodnight?
Not sure how helpful or new these suggestions are. From my perspective the bottomline is that no matter how young your daughter might seem, she is still facing what all humans must-- the trauma of change. That does not mean one has to change one's job for her, but rather to put on your thinking caps. How can you as parents help her deal with something that no one likes? How can you help her communicate her distress in appropriate ways? How can you make her feel safe and loved and protected during these times of change? How can you help her learn self-control and resilience, as young as she is, and support her in the need to outgrow temper tantrums and unpleasant acting out behaviors. There are many good books written on just this subject which might inspire you with better ideas than mine. Check them out.
Another good resource which people speak so rarely about today is prayer. Ask God to help you better understand and respond to your daughter's and family's needs and to help you grow ever more into a good, life-giving mom.
God Bless,
S.