I am in my 70s. I have always put on tefillin without a bracha on chol hamoed, following my father’s practice.
However, my father had a somewhat unusual practice ( which I have seen mentioned in an English sefer on the Halacha so of chol hamoed.) When he worked on chol hamoed he put on tefillin. When he did not work on chol hamoed he would not put on tefillin. This approach seemingly is not considered to be a halachic approach. My younger son has approached me many times asking about tefillin on chol hamoed. I have asked a number of times if I could be matir neder and stop this practice which seemingly was begun by my father in error. My father’s father came from Russia/Poland (Suwalki) alone in the early 1900s when he was sixteen. He was not shomer Shabbos and did not put on tefillin. My father became shomer Shabbos with the help of Rav Wertheimer and at least one other Rav in Borough Park. My father’s maternal grandfather took him on Shabbos to daven at the Trisker stible. My father’s family were far from being Chasidim.
Can I and my son be מתיר נדר and no longer put on tefillin on chol hamoed? Can my son on his own stop putting on tefillin on chol hamoed? Over the years I see many fewer men putting on tefillin on chol hamoed. In fact it seems that with few exceptions (other than Yekes) I am the only one wearing tefillin on chol hamoed. Incidentally, I have lived in Monsey for almost 35 years.
As you write, that you father’s family came from Suwalki, which was a litfishe Ashkenazi town, the minhag there was most probably to put on tefillin on Chol Hamoed. Therefore, that would be your family minhag, like the Rema, to put on tefillin. Therefore, the correct thing is that you and your children should put them on during Chol Hamoed, whether you are working or not. You can put them on for a minute at home, say shema and take them off.