I was born and raised in Ontario and have taken 3 budget (ish) trips from there to Disney. I consider myself a pro!!
I can help you calculate what you would need. It would be my pleasure to help! Since we now live in B.C. budget trips to Orlando no longer exist so it'll be a few years before I am able to return.
So, to start...we need to calculate expenses by each category, such as:
Food
Transportation--I'm not going to include this really since you are already going to be there for the dance competition
Lodgings
Spending
Tickets
The tickets is the one area where you can't really cut back much. Of course, the amount of days and type of tickets save you money and by buying from someone other than Disney you can save a bit, but not a ton.
2 day base passes will cost $724.20 USD for 2 adults and 2 kids
3 day base passes will cost $996.84 USD for 2 adults and 2 kids
It's after 4 days that you really begin to see the savings but on such a short extention, you'll have the above totals to work with.
All other areas have wiggle room depending on your choices.
Lodgings
Lots of ways to save here. One thing to consider though is that if you stay off site you have to have a way to get to the parks. If you rely on the hotels own shuttles (if they have them) they aren't always at the most convenient times and you often do a lot of waiting. A LOT. However, if you have your own car...you can come and go as you please but you WILL have to pay $15 a day (or more if they've raised it) for parking. But oftentimes the deals you can get offsite more than makes up for this cost.
FYI...3 nights at a value hotel onsite with 3 day base tickets will run you about $1500 USD...depending on dates (I plugged in July 24-27 in a standard room at POP Century). But if a deal comes up between now and then you might be able to save some money. (It would be about $1265 if you only got 2 day base tickets at "regular" price for the same amount of nights.)
You can priceline hotels (or use expedia or whatever) to get an idea of how much it would cost a night for an offsite hotel you'd be willing to stay in. We stayed offsite our first trip and booked through priceline and paid a mere $35 USD a night for a 3 star resort. Do watch for resort fees though...some of them charge for that and it ups the total room cost per night.
So hotel costs will vary, but let's put down $400 ($100 a night for 4 nights) just to be safe. Again, you can get rooms for cheaper than this with a little reserach.
That leaves food and spending.
If you pack lots of snacks (granola bars, juice boxes, nuts, fruit etc) and eat breakfast in your room, you can really eat on the cheap. But if you're only moderately careful...it's possible to eat lunch and dinner in the parks for about $100 a day (2 adults and 2 kids with average appetites). If you eat offsite, you can cut that back even further.
Since spending is rather personal...it's tough for me to calculate but we've gone down with $100 each and found that for a week that was more than. We've also gone down with a mere $50 each and that was enough for a couple of souveniers each and no one had any complaints.
So, to recap (based on 3 park days and 3 nights and the "max" amounts in each area to give us a baseline) you're looking at:
Food-$300
Lodgings-$300
Spending-$200
Tickets-$1000
So a total of about $1800 or less.
Staying at a value resort onsite would be $1500 plus food and spending.
OR (for 2 nights, 2 day base tickets)
Food-$200
Lodgings-$200
Spending-$200
Tickets-$725
Total of about $1325 or less.
Staying at a value resort onsite would be $1055 plus food and spending.
Check out this thread for idea on how to eat cheap at Disney:
If I only had $50 a day to spend on food at Disney!
HTH!! Good luck on fitting Disney into your budget!