Both of these are pre-emergent herbicides, meaning they will only kill weeds before they sprout. They are not effective against established weeds. Both are class III acute toxicity pesticides and are considered possible human carcinogens. Carsoron (active ingredient dichlobenil) is a persistent chemical, meaning it remains stable in both soil and water and isn't easily broken down. Dichlobenil is a broad spectrum, meaning it will kill grass and broadleaf plants. There are numerous environmental and health concerns associated with this chemical (see: https://wsdot.wa.gov/sites/default/files/2008/01/25/Herbicides-factsheet-Dichlobenil.pdf). Preen (active ingredient trifluralin) is known to be toxic to fish and other aquatic organisms, and earthworms (see: http://extoxnet.orst.edu/pips/triflura.htm). Considering your concerns about your dog, I would recommend using alternatives to herbicides to manage the weeds in your flower beds. 

Here is a response I wrote to a similar question last year:

The best method for weed control really depends on the types of weeds that you have. If you would like some help with weed identification, you can contact OSU Extension Lane County Master Gardener Plant Clinic for support (see https://extension.oregonstate.edu/mg/lane/have-gardening-question for more information). They can then provide some tips on how to control specific weeds.

I don’t know the types of weeds that you have (hopefully none that propagate vegetatively, like quackgrass or creeping bentgrass), so these are some general practices you can use.

Options for weed removal:

• Herbicides. If you decide to use a herbicide, always read the label prior to purchasing it to ensure the product will control the types of weeds you have, and follow the label directions for rates of application and other safety precautions. Spot spray if possible, rather than broadcast spray. Don’t spray on windy days, and avoid spraying plants that are in bloom (when bees are more likely to visit). Corn gluten is used as an organic herbicide
• Hand weeding. This is labor intensive but generally effective. There are some tools, such as stirrup hoes or collinear hoes that make it a little easier. Remove as much of the root as possible.
• Stale seed bed. Make the beds that you want to plant into and then water the beds. Allow any seeds stored in the soil to germinate, then remove the weeds. This will help to control the seeds in the top few inches of soil, but keep in mind the next time you turn or cultivate the soil, it will bring weed seeds up from deeper layers, so you may need to repeat this process. For more information on this practice, see: https://horticulture.ucdavis.edu/information/stale-seedbed-preparation, https://extension.umd.edu/learn/stale-seedbed-technique-relatively-underused-alternative-weed-management-tactic-vegetable
• Tarping. Cut back the weeds, and then cover the ground with a thick black tarp to block out sunlight and starve the weeds. https://smallfarms.cornell.edu/2019/07/manage-weeds-with-tarping/

Once the weeds have been removed:

• Mulching. After you have removed the weeds, cover your soil with an organic or synthetic mulch. Mulch will block out the sunlight and prevent weed seeds from germinating. Organic mulch options include straw (use straw, not hay which may have weed seeds in it), wood chips, cardboard (see sheet mulching), leaves (a great way to use up fall leaves!), or crushed hazelnut shells. These will decompose over time so will need to be replaced periodically. You need a 2-3 inch layer of mulch to suppress the weeds. A synthetic mulch option would be some type of weed mat (basically a synthetic fabric designed for use in yards). These also slowly break down over time, and need to be replaced about every 10 years or so (depending on the quality of the fabric). Synthetic mulches can be difficult to install when there are already plants in the ground.
• Perennial ground cover. There are also some perennial ground covers that suppress weeds (see this publication from Cornell for ideas http://cceoneida.com/resources/weed-suppressing-groundcover-brochure and talk to some local nurseries). An added bonus to ground covers, is that they also protect the soil from the impact of rain drops and prevent erosion, and they add some organic matter to the soil. A perennial ground cover would work best in areas that you already have ornamentals or other perennials growing.
• Plant spacing. Space plants so that their leaves will nearly touch at full maturity and therefore shade the ground (preventing weed seeds from germinating). Using plants with different plant heights also builds a canopy that will shade the soil. This can be tricky however, as you could end up shading out the plants you want, or creating a humid environment that is more conducive to pathogens. This method definitely requires some planning and knowledge of what the plants will look like at full maturity.

For more information on weed control in the home garden and landscape, see: https://pnwhandbooks.org/weed/horticultural/home-garden-landscape-management

There are some other options, such as solarization (but you need a really hot summer for this to be successful, https://local.extension.umn.edu/local/article/solarization-the-garden, http://ipm.ucanr.edu/PMG/PESTNOTES/pn74145.html), flame weeders (mostly effective against young weeds). However, as a home gardener your best option is to remove the weeds (using one of the methods listed above) and lay down a mulch or some type of perennial ground cover to prevent the weeds from returning.