Thanks for the question.

A few observations:

1).  Congratulations on planting clover.  It is a great attractor for insect-pollinators plus providing a natural way by which to introduce nutrients – especially nitrate – into the soil.

2).  The only explanation that I can provide to explain the difference between your front and back yards is the lesser amount of available sunlight in your back yard.  Before planting the clover, perhaps your back yard had less turf and more weeds than your front yard?

3).  I suspect that if there were weeds in your backyard before planting the clover, they were a mixture of annual and perennial weeds.  If the weeds dispersed their seeds prior to the clover planting in fall 2018, these seeds germinated this spring (2019) leading to the weeds that you have been observing. 

4).  Since you did extensive aeration last fall, there should be no need to repeat it again.

5).  For clover seeds to germinate, they must receive water every day for at least two weeks.  By the end of these two weeks, the clover should be over an inch in height.

6).  Any herbicide applied to your back yard to kill the weeds will also kill the clover.

Suggestions:

1). Since the weeds in the back yard are now actively growing, a broad leaf herbicide should be applied immediately.  This will also kill the clover in the back yard.  Perhaps the most efficient way to do this is using liquid herbicide that can be attached to your hose.  Be sure this herbicide contains one or more of the following:  2,4-D, 2,4-DP (dichlorprop), MCPP (mecoprop), dicamba, clopyralid, and triclopyr.  Repeat this herbicide treatment in late September or early October.  This should knock down most of the weeds.

2). Early in spring 2020, apply a fertilizer (NOT a “weed-and-feed” product). Then a few weeks afterwards (no later than the first of June), spread your clover seed.  Water it well for at least two weeks.  You should see clover shoots within a week. 

3).  Use a perennial white clover seed that you should be able to obtain at any gardening center.  Be sure to check the label to see that it contains 0% weed seeds.  There are no particular clover varieties of which I’m aware that are recommended for Minnesota.  Just be sure that the seed is intended for growing zones 4 and higher.  Do not use clover seed that is rated for growing zones 5 and higher.

One final point.  In any yard in which clover is desired, the use of broad leaf herbicides should be avoided unless that herbicide explicitly states that it is not effective against clover.  Otherwise your weed control will consist of manually pulling the weeds.  Of course, a dense growth of grass and clover will be a great weed deterrent.

Please let us know if you have additional questions.  Good Luck!!