I could say (that) I have the'm lucky that a lot of things or moments, do they make me happy.

In my revision, a lot of times we'll omit the first "that" (the one in parentheses). If I were talking I would just say, "I could say I'm lucky that...".

WFor instance, when I get home and I see the face of joy ofn my wife, for instan's face.

You can put "for instance" at the end no problem. I just put it at the beginning since I think it's a little more common that way, especially when speaking.

I have never seen any dog docausing any kind of problems.

We usually say "causing" problems instead of "doing" problems.

Unfortunately, with people, I can't tellsay the same.

Also I like muchreally enjoy my trips by bike along the beaches ion a sunny and peaceful morning.

We don't typically say, "like much". I would say something like, "I really like..." or "I really enjoy..." instead. Either one sounds more natural to me. I put "really enjoy" in my correction because it's the one I'm used to hearing the most in these kinds of situations and the one I would say if I were speaking, but "really like" works too.