You do indeed have an unabridged Haydock Bible!

If the Bible is in poor condition I would recommend having it restored by a competent binder. It may be pricey, as much as 3-4 hundred dollars for a good job, but afterwards you will have a priceless heirloom leather bible that will last another 150 yrs. if cared for. It will also make reading your Haydock Bible far less scary, since you can use it as easily as any huge Bible.
I have several (5 to be exact) dating from 1825 through 1910 and a 2014 reprint. All of them are either in excellent original condition, or they have been restored. My favorite one for reading is the Oakeley Haydock from 1910. It is a rather unusual version in that it is based on the Canon Huesenbeth abridged Haydock notes, but is then updated with new additions. So in effect represents the latest, most up to date Haydock version. It was first published in London in 1878.
Anyhoo, your Bible by Dunigan is also rather unique. It uses an eclectic update and correction of the Haydock text (which was based on McMahon’s correction of Challoner’s Bible.) Cardinal Newman had this to say about the Dunigan Bible (which first appeared in 1852-1856):
1852-56. This splendid edition, which is published by Messrs. Dunigan of New York, in quarto, is introduced to the public by those many high approbations and recommendations to which we have already referred. Dr. Cotton says that “it appears to have been copied from Haydock’s first impression of 1811.” We do not know how to follow him in this conclusion; but we have not been able to find any information on the subject in the edition itself. Our {439} reason for questioning Dr. Cotton’s belief is, that, on taking twenty instances of text at hazard in the editions of 1811-14 and of 1852-56, we found the latter to differ from the former in seven, of which four are altered back to Challoner’s editions, one agrees with Cardinal Wiseman’s, and two with no edition with which we are acquainted.
Later we learn that an American Priest (also named McMahon, James) collated and corrected the text, making it unique.
Now as far as reading:
I also have the Personal Study Bible (NABRE), the 1966 Jerusalem Bible (study bible), the Ignatius Study Bible (RSV-CE2) and of course the Haydock Bibles. (I’m not counting all of the stand alone Bible commentaries

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Reading a Haydock Bible is actually reading the Douay/Rheims Bible, updated/revised by Bishop Challoner, and further revised by McMahon, and yet again by the American McMahon. Sometimes the text is wonderfully familiar and classic. Other times it can be obscure and difficult to comprehend. The notes may help in some cases but not in others. So what I do right now, in Easter Season, is to read my Ignatius Study Bible, since most of the liturgical readings are from the NT. I use the Psalms from the NABRE. But after Pentecost I will probably start using the Haydock Bible again.
In any event, I would recommend having those newer bibles as well, as there are many situations where the newer bible has a clearer meaning, and even more helpful notes (not to mention special essays and maps)