Other posters here are right -- it's important for both children to learn and understand that life is not going to be this perfectly fair, perfectly balanced, always "even" score between them. If one gets X, the other should not necessarily get X. You and your guy will have to accept this YOURSELVES first, though. If the kids realize that you and dad are feeling conflicted and guilty over one child not getting what the other one has, believe me, even if they are the nicest kids in the world, as they get older they will at times use the adults' guilt to get things they want.
Also: Your So What Happened mentions that dad "tends to baby" daughter sometimes. Please, please work with him to end that. He is in serious danger of becoming "fun dad" -- that guy who lets the child do anything and everything when she is with him because he feels guilty he doesn't see her all the time. Fun dads are great from the kid's perspective -- who doesn't love a great outing every single time they're with someone! -- but fun dads do a lot of damage to their own relationship with the child. The child will learn that dad is pretty much nothing but a source for entertainment and material goods, and will be less and less able to accept discipliine or "No" from dad. Fun dads also damage their ex's relationship with the child, because the child feels like this: "Why can't mom be fun and say yes to things like dad does? I'd rather be at dad's where I don't have chores, don't have to get up early, etc." One parent becomes the bad guy and the other the all-fun, all-the-time parent, and both households suffer.
And with that said...Be sure BOTH children are equal and balanced in one thing: Your expectations of them in your home. Both should have age-appropriate chores they must do; both should be expected to show the same level of respect and listening; both should have the same sorts of schedules when they are with you, alone or together (don't let one sleep in every time while the other is expected to be up and busy, for instance). THAT is where dad needs to ensure balance. But if he wants to coddle his daughter, not only will your son see that and feel angry and slighted, but his daughter will become harder to handle.
So...no, dad should not spend money he does not have in order to make his daughter feel "equal" because son was given a gift. Sure, take her to an inexpensive nail place for an hour as a treat, or just out for ice cream (not every day!), and to the park a lot. But don't frame it as "we're doing this BECAUSE Joe is in a cool camp and you're not" and don't frame it as "We're doing this to make up for the fact Joe's in camp...." Let it be about "We're happy to spend time with you and anything we do together is great." But don't haul her off on a trip just because dad feels you must. Besides, why teach a child that it's OK to spend what you don't have?