What's your question? Ask

Here is an article that you may find helpful: https://www.gardeningknowhow.com/special/organic/homemade-pet-friendly-weed-killer.htm

Here's a recipe that may help using 1 gallon of white vinegar, 1 lb. table salt, and 8 drops of liquid dish soap. Mix the vinegar and salt in a pan on the stovetop. Bring to a boil so that the salt dissolves into the vinegar. Remove from stove and stir in the dish soap. Allow the mixture to cool. Pour into spray bottle and use a stream setting to aim directly into the middle of the dandelion rosette so that you do not kill the surrounding grass. Dandelions should die within a day.

If you are killing weeds, the normal vinegar that you buy from the store will do. There is no need to dilute it as it is already diluted when you buy it. And, the vinegar from the store will not harm your dog. Here's a recipe that may help using 1 gallon of white vinegar, 1 lb. table salt, and 8 drops of liquid dish soap. Mix the vinegar and salt in a pan on the stovetop. Bring to a boil so that the salt dissolves into the vinegar. Remove from stove and stir in the dish soap. Allow the mixture to cool. Pour into spray bottle and use a stream setting to aim directly into the middle of the dandelion rosette so that you do not kill the surrounding grass. Dandelions should die within a day and it won't harm your dog.

This article should help as well: https://www.gardeningknowhow.com/special/organic/homemade-pet-friendly-weed-killer.htm

Yes, the same would apply for the lawn. Simply spot treat wherever necessary. These articles on dandelions and wild violets (most likely your purple flowered culprits) should offer suggestions as well: https://www.gardeningknowhow.com/edible/herbs/dandelion/dandelion-control.htm
https://www.gardeningknowhow.com/ornamental/bulbs/violet/kill-wild-violets.htm

Here's a recipe that may help for both types of weeds using 1 gallon of white vinegar, 1 lb. table salt, and 8 drops of liquid dish soap. Mix the vinegar and salt in a pan on the stove top. Bring to a boil so that the salt dissolves into the vinegar. Remove from stove and stir in the dish soap. Allow the mixture to cool. Pour into spray bottle and use a stream setting to aim directly into the middle of the dandelion rosette or violet, so that you do not kill the surrounding grass. The weeds should die within a day.

Here is an article that you may find helpful and is safe for both pets and children: https://www.gardeningknowhow.com/special/organic/homemade-pet-friendly-weed-killer.htm

Here is an article that you may find helpful: https://www.gardeningknowhow.com/special/organic/homemade-pet-friendly-weed-killer.htm

Also, here's a recipe that may help using 1 gallon of white vinegar, 1 cup table salt, and 8 drops of liquid dish soap. Mix the vinegar and salt in a pan on the stovetop. Bring to a boil so that the salt dissolves into the vinegar. Remove from stove and stir in the dish soap. Allow the mixture to cool. Pour into spray bottle and use a stream setting to aim directly into the middle of the dandelion rosette so that you do not kill the surrounding grass. Dandelions should die within a day and it won't harm your dogs.

Using a good weed and feed fertilizer should get them under some control. However if your neighbor does not do the same, they will likely keep coming back.