Meds in the water wouldn't hurt the fry, IMO, it may help them fight off whatever the parents have. But this is speculation on my part, I don't have actual data.
I'd do whatever is easier for you as far as the tank for the two adults. Either keep them where they are and add some live rock and macro, along with a decent filter, or put them in the 14. I'd be very careful about temps though. Higher temperatures seem to bring on recurrence of tail rot and other infections in recovering seahorses.
Fry need to be raised in a totally different type of system than adults. Usually involving just an airline, possibly in co-culture with phyto and rots. Other people use sterile systems with an airline and frequent water changes. Often, small tanks or buckets work well for fry, or people use kreisel systems. You can apply clownfish fry practices to some extent.
If you don't have the time, I'd adopt out the fry (or dare I say it, flush them). Even under the best conditions, raising pelagic fry is not easy. You've had your hands full taking care of the parents, fry would make it all that much harder.
Good luck!