Greetings Belinda:
Appears you may need to guy and stake the tree in the front yard. Insufficient root growth, top heavy, planted improperly, saturated soils, etc. could all be reasons for the "rubbery" appearance.
To learn how to stake and guy a tree, please refer to the following publication:
http://www.ces.purdue.edu/extmedia/FNR/FNR-FAQ-6.pdf