Sorry to hear about this, not sure I have very much sensible advice but hopefully by bumping your post up a bit someone will be along who can help!
You say this is all 'recent', how long has it been? It's very common for little ones this age to be unsettled when starting childcare, whingy, clingy, over-tired etc if they are not used to being away from parents/home at all and it can take weeks for them to settle in. It may be you just need to give her lots of love and reassurance and stick with it and things will improve. How is she once actually at pre-school/relatives, is she anxious/crying throughout or is it only when you arrive/leave that she is upset - sometimes transition is the hard part and actually once Mum is out the door and they settle down they are fine - really hard for you though to see her upset so consistently!
If things have been this way for a while and she really isn't happy, perhaps you do need to make some changes, I wouldn't leap to giving up work necessarily, for me in the long-term I think most people (not saying all as everyone is different) it is best for them financially and in terms of self-worth and long-term prospects to have some kind of career, and what is good for you will be good for DD ultimately. So you certainly aren't being 'selfish' for wanting to work. However it does sound as though she goes to a lot of different people to be looked after (preschool and different relatives every day), also have I go it right that you drop her at pre-school, then pick her up and drop her again at relatives, if it is the transition/handover she is finding hard then that could explain it as that's 4 different times it happens in the day - is there any way you can reduce this? E.g. could you find a local childminder who she could go to instead of the relatives or the pre-school, some childminders will do drop off and pick up if needed? I think it would help her a lot having a simpler/more consistent routine. Or could you drop the pre-school altogether, obviously there are a lot of benefits to early education but if your DD isn't ready and is upset throughout then she may not be learning much anyway, lots of children are just better off in a more homely environment and it doesn't seem to adversely impact them later on IMO. Using a registered childminder means you are eligible for tax credits to help with the costs if I remember correctly. Or would one of your relatives be prepared to have her more often, perhaps if you paid them (I know there are complexities with paying relatives for childcare but it's not impossible)? Or could you keep the job but ask to change/reduce your hours slightly - I know this is tricky with a new job but you could always ask, don't ask don't get!