The plastic covered homemade covers are surrounded by sand bags so although helpful not a permanent fix. They do prevent direct rain from coming in through the main opening. The backyard slightly slopes towards the back of the house and water though limited will still find a way in until better drainage is established.
Retired plumber here. It sounds like you need a french drain installed. There isnt really all that much to it as far as expertise is concerned, it's mostly just a lot of expensive labor.
But if you wanted to do the labor yourself, I could walk you through the process of doing it.
IThe water comes in the back wall? So you dig up all along along the foundation outside about 4 ft deep all along the foundation of the house. Lower than ground level in the window wellsand you put down a bed about 4 inches deep of large gravel and lay the french drain pipe (The stuff with holes already in it!) and run it from one end of the house to the other end, starting high and giving it grade for drainage and at the far end of the house you sink a sump pump pit into it and dump the pipe into the sump pit. The sump pit top falls out at ground level. And it's underneath the windowwells so the water level never rises to ground level. Then you top off the pipe with another 6 or 8 inches of large gravel and back fill the ditch.
But! After you dig it but Before you start running gravel and pipe, you seal the foundation wall with black sealant. Then do the pipe and back fill. I used to charge people 5 to 7 thousand dollars for this type job, so your labor will be well spent! Hope you have Boys to help you!
Oh and you would have to use pvc pipe to pump the water way out into the yard somewhere too. Only rarely did we have to install a concrete culvert too, but that's possible to get it out to the street or whereever.