It can certainly be a bit risky to offer any absoulte answer to the question the lady posed, so your question is a very reasonable one. As a general rule, though, it is not a good idea for a very young child (particularly during the first year or so) to have the sort of overnight contact the lady described. This is especially so when the 'visit' is going to be for an extended period of time and with a parent (whether mother or father) who has apparently not bend dedicated to consistent, regular contact over the child's early life. Your note implies that you have been a very active, involved, attentive parent, and that sort of circumstance can call for a different conclusion, depending on the particulars.
I am curious about the line of advice provided here. From the question I gather there has been some friction between the mother and the father, however, this is an assumption on my part. Regardless, as is pointed out by the mother, the move and the limited visitations have been the choice of the father. There has been nothing indicating a lack of ability on the father's part to care for an infant. 3 1/2 months is awfully young, however, UNLESS the mother is strictly breastfeeding; I am curious as to what grounds makes a weeklong visitation so damaging to a child so young?
However, be advised, I ask this question from a loaded point of view in that my ex wife and I divorced while my oldest son (now 10 years old) was just a baby, and I had extended visitations during which I was able to provide adequate care for my son. Since my son at age 10 is a straight student, and appears very well adjusted and extremely intelligent for his age, I have to point out that my extended visitations and his being away from his mother has not had any adverse effects on him.
The plan your son's father is suggesting is definitely out of the question for a child so young. The plan for him to visit in Arizona can be much more flexible, provided he is not taking the boy for overnight. Weekly or alternate weeks or once monthly, all would be suitable. It might make sesne to have a guardian ad litem apppointed for the express purpose of advising the court on a visitation plan, particularly since the plan will change over time (provided his father keeps up contact), as the boy grows older.