Hi Larisa! Splitting your stay between two resorts is a fun way to experience different areas of Disney World, but you've hit upon the main drawback of a split stay. At your first resort, you can purchase park tickets to cover your entire
stay at both resorts, but you 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. In my experience, however, it generally isn't cost effective, and if you want the Dining Plan for your entire vacation, you're better off with one resort. When my family splits our stays, we generally don't buy the Dining Plan.
Hope this helps!