Hi - decide how you want to spend your time, and where you want to be. ; If your youngest is under 3 when you visit, you won't have to pay for park admission or dining (if you get the plan) for them - so that's a savings.
Don't know about specials for Jun.10 yet (current special doesn't go that far in planning window ; - it expires Dec.20) but the great thing about working with Disney directly is that you can put $200 USD down to secure spot, and your trusty travel agent (ahem) can apply any specials that come on after you book (if availability) - balance is due 45 days before you go.
I always encourage folks to stay onsite. ; There are opposing views, but in my 17 visits, I've stayed onsite and offsite - to my mind, the benefits of onsite far outweigh the benefits of offsite.
Disney has 22 hotels onsite to fit every budget. ; THe benefits of staying at onsite include access to extra magic hours (huge deal), ability to buy dining plan, free shuttle to and from airport, free transportation around the parks, being surrounded by magic, ability to shop at parks and have purchases delivered back to your room, etc., etc.
With your two wee ones, if budget is foremost in mind, then the onsite value hotels are best option - Pop Century is very popular. ; Look at pictures of the All Stars though - because the theming might appeal to your kids more (everyone has different tastes) - there's the AS Sports, Movies, Music. ; If you want a little extra space, the AS Music has a family suite that gives you 2 bathrooms, microwave & stove, and extra room.
WIth moderate level, you might want to look at Fort Wilderness Cabins - self-contained, own BBQ, kitchen, etc.
With deluxe, you have 3 monorail hotels (ease of access to MK park and/or Epcot on monorail, plus Contemporary is walkable for little kids from Contemporary). ; THe DVC spots have more room, essentially are timeshares that rent out as hotel rooms to public - condos, with extra room, kitchens, etc. - but are priced accordingly too.
That's an overview in a nutshell. ; Any questions, or anything I can help with, let me know.
Best regards,
Sheila