Hi Sherri! My family loves to split our stays so that we can experience different resorts, and you've picked two of my favorites! While there are lots of benefits to moving from one resort to another during your vacation, one drawback is that the dining plan doesn't easily move with you. At your first resort, you can purchase park tickets to cover your entire stay at both resorts, but can purchase the dining plan only for the number of nights you're staying at the first resort. Your dining plan credits must be used by midnight of the day you check out of the first resort.
Unless you're an annual passholder, in order to purchase the dining plan at the second resort, you must buy park tickets for everyone in your party. You could purchase just a one-day ticket, but you're probably aware that with Disney park tickets "the longer you play, the less you pay per day." The one-day ticket is the most expensive, and with every day you add, the price per day decreases, so that after the fourth day, you're paying only a few dollars more to add days to your ticket.
You'll need to do some number-crunching to determine whether purchasing the dining plan at both resorts would be cost-effective. You'll likely find that it is cheaper to purchase park tickets for your whole stay on the first resort reservation, rather than paying for shorter-term tickets at each resort. The question then becomes whether it's worth it to buy a one-day ticket for everyone in your party at the second resort so that you can add the dining plan. If you think the savings you'll have on the dining plan will outweigh the cost of the additional tickets, it would be worthwhile. (Keep in mind that if you don't use the one-day tickets, you could save them for a future trip.)
Hope this helps!