First there's tips for TS meals...Dining plan doesn't include gratuities so figure about 18-20% of bill (including buffet meals). If you want to get an idea of what meals will cost you can check out the menus for the restaurants you have ADRS on allearsnet.com to get an idea of how much you need to budget for tips. Also you may want to also tip housekeeping. Around $5 a day is what we usually leave.
Then there's additional food outside of plan. Only you know the type of eaters you and your son are...will what you get on the dining plan be enough food each day or do you foresee needing an additional meal / snack each day? If you see an additional meal then maybe you should decide with your friend how many , if any, additional TS meals you will have...for easier budgeting you may decide to stick with TS meals from dining plan and any additional food / meals will be CS or snacks.
Snacks can cost between $2.50 (sodas) to $5.00 each (really big treat). Most are around $3.50 - $4 price range.
CS Meals can be around $10 for adult $6 for child give or take depending upon what you order (check out allearsnet for prices to get a better idea).
In addition to dining the only extra costs that you may have to budget with your friend is if you plan on doing any extra events / activities such as mini golf, renting recreational boats. etc. There's plenty to do in the parks without having to pay for extra activities and if your friend wants to do a spa or something she can do it and meet up with you later on.
Outside of dining and activities, I think any other spending you do is to your discretion regardless of what your friend spends. As far as souvenirs decide on a budget that is comfortable for you. And maybe instead of telling your son you will buy him 1 toy per park maybe you can get him a Disney gift card for an amount within your budget and he can use that gift card for whatever souvenirs he wants, but that's all he gets to spend. If he wants, he can add some of his own money to the card.
I don't figure budget as a daily cost more like a category cost...like
$$$ for tips (meals, housekeeping, ME, bell services, airport)
$$$ for food (additional snacks and meals to DP )
$$$ for additional activities (video arcade, mini golf, tours, etc.)
$$$ for souvenirs