Yes it can be normal for parents to react the way your mum has.
My mum doesnt want to me go to uni far away, but i feel thats because she relies on me alot to babysit etc! Im worried about going to uni because i dont know how my household will survive without me. i do alot of the cleaning, washing, feeding and looking after my brothers, especially the youngest, hes 4.
Yea your mum will miss you, but its your life, your growing up and its time for you to gain your own independance! I dont think she is showing you shes upset to make you feel bad though. Her child is growing up and shes just struggling to come to terms with it!