Ive never stayed in the airside hotel so I do not know what it is like. Best bet may be to get a hotel in Deira, they are generally cheaper than those in the Marina district especially in the summer.
The immigration queues at DXB should be bearable at 1300 unless its a local holiday. Deira is about 15 minutes taxi ride from the airport (sometimes a little more, sometimes considerably less in quiet times).
A tip when going back to the airport is to check in online and print out your boarding pass. If the airport is busy it will save you alot of hassle.