I dislike item roll suggestions without formula support. So, regarding CHD versus ELE on that ring, imagine you have a weapon with 1000 max damage, 9500 INT without the ring, and currently have 0% CHD and 0% element.
If you rolled the ring to max INT
1000 weapon * 100 (equal 10,000 %) dmg modifier from primary stat = 100,000 on regular hit
If you rolled the INT to 50% CHD
1000 weapon * 95 (equals 9,500 %) stat mod = 95,000 on regular hit
1000 weapon * 95 (equals 9,500 %) stat mod * 1.5 on crit = 142,500 on crit hit
If you rolled the element to 5% and also had 400 INT
1000 weapon * 99 (equals 9,900 %) stat mod * 1.05 element mod = 103,950 on regular hit
We're saying "5% element" in this last equation just to simplify the math. In actuality all of the equations would have a 1.15 element mod (and 1.2 in the last equation). However, because it is a modifier common to all equations, we can eliminate it without changing the comparison.
Now, let's look at the damage output over a series of hits, assuming 50% critical chance.
(95,000 + 142,500) / 2 = 118,750 average damage per hit
The other 2 options don't need to be averaged. They are always going to produce the same damage per hit (in reality, the damage range on the weapon will produce varying damage, however we'll ignore that). That means the average hit is always going to be 103,950 on the ring with +5% element and 100,000 with max INT.
Ergo, rerolling the elemental damage mod is more valuable than gaining 100 more INT (assuming you are always using attacks that utilize the +element modifier). Likewise, rolling 50% CHD is much more valuable than either of the other two options.
The only remaining doubt would be if attack speed is not valuable in your build. For instance, attack speed is not very important for some types of Wizards and Witch Doctors. In that case, attack speed would be a better choice to replace than INT. However, as we're talking about a Pet Doctor, AS is valuable.