Wifi Issues with Two Routers

[NaterTater]

I brought an Asus RT-AC3200 wifi router to my new two-bedroom apartment. However, this apartment comes with a router, and we have to use their router and internet without admin privileges. They tucked their tiny router in the utility room in the corner of the apartment, so I thought I would set up my nicer router as a range extender near the center of the apartment. I connected my router to theirs with the built-in ethernet ports in the wall. I thought that this method would:

 1) provide better coverage

 2) keep me from having to set-up all my wifi devices over again (I kept its old name which is different from the new router's network name.)

 3) keep my router from sitting useless in a box

Unfortunately, I frequently have very slow internet. I don't know what to blame or how to fix it. I have 25Mbps download from the provider, but today was having trouble streaming 720p video with only one device online. Speedtests usually confirm I am getting the correct download and upload speeds in this configuration, so I don't know why I have such trouble loading and streaming sometimes. Can the routers interfere rather than help? Is keeping the old router name and connecting my devices to it a bad idea? Any settings I could have configured incorrectly? Did I do everything perfectly and it's all my provider's fault? I only have very basic networking knowledge, so any thoughts would be appreciated.