Work in Progress
-
---
$E$ and $I$
>! Visited on Saturday, February 10th, 2018.

$D$ and $G$
>! Visited in February on the 21st or 28th.

$J$ and $A$
>! Visited in March on the 3rd or 10th.

$C$ and $B$
>! Visited in April on the 21st or 28th.

$F$ and $H$
>! Visited on a Saturday, $28$ days before $A$.

---
Reasoning
-

$A$ not after $J$ but $28$ days after $F$.
>! This tells us that $A$ cannot visit after $J$ nor before $28$ days after $F$ has visited. Thus the smart thing to do is to pair $A$ with $J$ since this is not technically after $J$ (which threw me off as I was avoiding the pairing until I read the phrase more carefully).

$J$ in **March**; at least $50$ days prior to $C$ on the same day of the week.
>! This tells us that $C$ comes after $J$ and that $J$ is in **March**.