Hi Natalie,
9.25" is pretty big, and for that size/budget you would generally be looking at a newtonian or a Schmidt Cassegrain (SCT) design on say and HEQ5 Pro or HEQ6 Pro mount.
Now you already mentioned about the alignment (collimation) of the newtonian mirrors has been an issue, so perhaps an SCT would be better for you all for a couple of reasons....
1) The tube is MUCH shorter and more compact than a traditional Newt
2) Less fiddling around with collimation (not that hard really), but less overall.
3) GREAT scopes for planets as their longer focal length compared to newts allows for higher magnifications. For example, my 200mm (8") newtonian has a focal length of 1000mm which makes it an F5 scope and with a 10mm eyepiece, I get 100x magnification (FL/EP). Now on say a CPC Celestron 8" SCT has a focal length of 2000mm which means you would get 200x mag from the same 10mm eyepiece. This is due to the folded light path design of the SCT.
4) Shorter SCT design means easier to handle and view through. Tube Length of the SCT mentioned above is around 17" or about 430mm. In comparison, my 8" Newt is over 1000mm long and the eyepiece position changes depending on where it is pointing on the Equatorial mount. On an SCT, the focuser is on the back and stays there no matter where it points.
5) Having an EQ mount means you wont get field rotation of the object you are looking at for AP. Fork mounted SCT's are effectively Alt AZ mounts meaning what ever you are looking at will slowly rotate in the eyepiece over time, meaning AP is harder or you have to buy an expensive and fiddly de-rotator to compensate.
Now, I am not an expert by any means, just some info I have gathered over time, more experienced members will chime in no doubt to correct anything I may have overlooked or got wrong.
FYI, I have a 8" Black Diamond newt on an HEQ5 pro which sells for around $1400 from Andrews Comms. Based on your budget of $3K, this is around half, this scope is MORE than capable of visual, goto, AP and deep sky objects and by having $1500 left to spend on cameras, coma corrector, filters, adaptors and eyepieces makes it a very nice bang for your buck price point to get you started.
The goto and computer control as well as the fast F5 ratio mean that my inner geek is kept happy and I can take AP shots quicky and cheaper than an expensive rig (although at a lower quality, obviously), after all, you do get what you pay for, however, it is not inconcievable to spend $5-6K on a serious AP rig if you arent careful.
Here is a post discussing my purchase as well as a pic of the rig with me standing next to it, I am 6 foot 9 and the tripod is all the way down, so you can see it is not quite the smallest thing, one reason why I suggest an SCT for your daughter....
Hope this helps,
Cheers
Chris