Time outs won't work with a two year old who is angry and frustrated C.. Her world is difficult right now... day care every day and a new brother to boot. Kids don't like transitions at this age and they don't respond to time outs or discipline (riding in the wagon alone). What she really needs is more time at home and with her family.
Is there nothing that can be done to give her a break from the pressures of day care? How much time at home does she get each week? I would suggest that you give consideration to the real life experience your daughter must be having... it sounds like the safety of home is not translated to her Monday-Friday experience.
Actually, it sounds like she hates daycare. A new day care or a chance to stay home for a while will calm her down and help her through this stage. She'll only be a toddler once... is there no way to make this a fun, happy time for her?