Can i be evicted for not getting along with my neighboor? Please help we are desperate!!!!!?

we moved into a duplex a little over a yr. ago. Our neighboor is a retired lonely older woman . We were severely warned by the previous tenants that she was a handful to deal with. But against their advice we moved in. She has continually complained about petty things like my 8 yr old son making noise while playing. Especially about my son "agrivating" her cat, or our cat agrivating hers, to the point that we keep our cat indoors to avoid any conflict. Now our land lord called and said my son agrivated her cat again. Also there was a parked car w/ no licence plates in the front of the property, we didnt know whos it was , it was in the way so we asked whoever it was to move it or we would have it towed. Well it was her son in laws so she said we were rude to do that. My landlord said he would have us both evicted if we could not get along. Is this legal? he also said that if he found any pesticide on the property it would get"serious" but he did not include this in the lease? what are our rights her please help!!!!!!