You did not mention any triggers so I will interpret it in a general sense. Usually, dogs speak of backsliding, but, in some cases, it speaks of a specific person who will cross your path.
So in this case, the brown dog symbolizes a person who is living a sinful life (immorality and laziness). This person is also suffering because of other people sucking everything out of him. I do not know whether it is financially or with regard to resources or a particular thing that he or she has that people want. There are many of them and they are all in one area, probably all seeking the same thing. The fact that he has only three legs speaks of him not being able to cope with the situation (weakened spiritually).
You pushing him forward speaks of you helping him although he or she may not trust you completely (snapping at you). This person does not trust people because, based on his experience with people, they all have hidden and bad motives. You trying to remove the ticks speaks of you trying to help him get rid of those bad people.
A tick symbolizes a person who is drawing excitement and inspiration from others. It speaks of people who act like parasites. They suck all energy and life out of other people.
The clown speaks of people who are keeping themselves busy with all sorts of enjoyment and pleasure instead of being serious about life. This attitude or motivation is also part of this person’s world. This person needs help. Spiritual help. He needs God and he needs to repent or he or she will be destroyed. He is already in a bad shape spiritually.
Somebody close to you, probably your wife, favors this person. She wants you to help him.