Lou, a lot of what you have said is not correct at all.

"I have a dog" is not an infinitive, as you suggest. It is merely a verb conjugated in the first person singular.

Infinitives always take the preposition "to". The infinitive is 'to have".

You have then suggested that "I used to have a dog"  means the same as  "I had a dog".

In fact, these do not have the same meaning.

"I used to have" is the English equivalent of the past imperfect tense, whereas"I had" is the past simple tense.

Strictly speaking, we do not have an actual past imperfect tense in English, so we often use "used to + verb" instead.

Terry, it has nothing to do with being a native speaker or not, and everything to do with whether or not one has a basic knowledge of grammar.

The past imperfect tense and the past simple tense are used to convey different meanings.

(Again, I should stress that, strictly speaking, English has no past imperfect tense, so we often use "used to + verb" as a kind of substitute for it).

You may think that it is the same thing to say "I had a dog" and "I used to have a dog" but it does not mean the same thing at all. Compare:

"I had a dog yesterday for the day, because I was taking care of it"  This means you were dogsitting for somebody (for one day only).

"I used to have a dog of my own, but it died"  This means you used to own a dog (for a long duration of time).

You could not say "I used to have a dog yesterday". That would not make any sense. It's true that you can often substitute "used to have" for "had", but it does not work the other way around.

Another example: try substituting "dog" for something else: "hot dog" for example. 

"I had a hot dog yesterday" means you had ONE hot dog, on ONE specific occasion.

"I used to have a hot dog every day" means that in the past, you used to have a daily routine of always eating a hot dog every day.

When you say "Southern English" do you mean "Southern American English"? You can't just say "Southern" and expect everybody to know what you mean. North, East, South and West are just points on a compass. 

Hi. As a native speaker of American English, I have to say that "I used to have a dog" and "I had a dog" mean exactly the same thing. True, they are not the same tense, but they both indicate action that was begun and completed before the time of speaking. The "used to have" kind of construction used to be more common in southern English but is more widespread now.  You can almost always substitute the "used + infinitive" for the simple past of just the infinitive.

Example: used to have = had

used to be = was

 used to go = went

used to sing = sang

There is a VERY slight difference in meaning. The used + infinitive construction indicates a past action that continued for a while, where the simple past could (but not always) indicate a one-time, momentary action.