Siblings

I have two daughters 9 and 3. Since my baby was about 6 months she has wanted nothing much to do with her sister. She couldn’t hold her, play with her much or even push her in a shopping cart without her screaming to escape. Although she loves her because whatever the 3 yo has she makes sure her sister has it also. She defends her even when I discipline her telling me “don’t make my sister cry”. At home it’s a CONSTANT fussing, fighting and arguing. The personalities are very different. The 9yo is humble and very easy going. Will this end or do you feel my girls won’t be close siblings. This worrying me b/c if anything happens to me I want them to be there for each other.