S.B.
WE installed a french drain for our standing water issue. We had to dig a trench from our back yard to the front. Put in the pipe, cover with gravel and rock and then cover back up with the dirt. We have neighbors that actually had to install a sump pump in their yard.
My experience with ground cover is that most need good drainage to do well.
A trick for the mosquitoes in the mean time....drop a bath bead in any standing water. The oil will help stop the mosquitoes. We dropped some in a neighbors yard who refused to do anything about the standing water, we got permission first. It helped cull the population.
There may be a lot of reasons for the standing water. It may be worth making an appointment with a landscaper to find out what can and needs to be done. You may find you can do quite a bit yourself. Hurry...with this crazy weather this season, those 100 degree days are right around the corner!