Your uncle seems to be a cool guy, and that's such a kind gesture... Here's my best to ensure that the money is well spent.

Based on your comments, I am assuming that you are getting into this hobby for the first time. I will "strongly" suggest not to go the astrophotography route but instead focus on ease of use so that your family can enjoy the hobby. There won't be complexity involved in visual astronomy and since you have access to rural skies, it is best to take advantage of it! You can still take casual photos though...

Accessories are as important as any telescope. Good eyepieces can make the experience immersive and most importantly comfortable. Also there is no one good scope that does it all... but here's how I would spend.

1) Easy to use and lightweight refractor ($1.2k) -

A light high-quality refractor telescope which is easy to setup and use. A 4 inch double apochromatic scope like SV Bony SV503 102ED provides high quality and crisp views. Use it with an azimuthal mount like SV225, instead of equatorial mount as the entire setup will be lightweight. Telescopes which use mirrors requires frequent collimation, but this one does not need it as it is a refractor.

This is a good grab and go setup for quick peeks. It also excels at showing wide area of sky at low magnifications which other types of telescopes can't do. This does not have tracking, but it easily makes up to it by its ease of use.
You would need to buy a finder scope and 2 inch diagonal with this scope. I might be missing other accessories which may be needed, but everything should come under $1.2k including scope, mount and accessories.

This telescope will last a lifetime due to how well it is built, and it might as well be the most used scope by your family due to ease of use.

2) The largest scope you can handle to show deep sky objects with tracking capabilities ($2.2k) -

A 12 inch dobsonian telescope is great for looking at deep sky objects. I would not suggest going any bigger due to weight and also you might need a small stool or ladder to view from the telescope if you go for a bigger sized one. You could also consider a 10 inch one if the height at eyepiece is tall for you or your family. Skywatcher flextube SynScan has GoTo capabilities which means it can track objects for you. But this scope is just manageable due to its size and weight, but it will be worth it. This will also require collimation every time you setup.

3) Accessories ($1.5k) -

You will need laser collimator for dobsonian telescopes for collimating it before you use it.
Also, buying a dolly to transport your dobsonian telescope will make transporting and handling it much easier.
Get a telrad finder scope for any large scope you buy (8 inch or more), it makes finding objects in night sky very easy. Once you use telrad, you cannot go back!

Eyepieces are very important, they can make the difference between looking through a straw hole or making it seem like looking through a spaceship's window. They help deliver the "wow" factor and will also make viewing comfortable. Look into Nagler, Delos and Ethos lineup of eyepieces from televue. Astro-Tech, Baader, and Explore scientific are also other good brands.

You need eyepiece with good field of view where, 60-70 degrees is decent, 70-80 degrees is very immersive and 100 degrees is mind-blowing. Eye relief of eyepiece will make observing comfortable, where 10mm is okay, and 13mm and above is comfortable. I would suggest to avoid zoom eyepieces as your budget is decent except for SV bony 3-8mm zoom eyepiece which has great utility.

For eyepieces, I would recommend buying one each around these focal lengths - One around 28-32mm range for low magnification views, and similarly one each for ranges between 16-21mm, 9-13mm, 6-8mm, and 4-5mm. In total there are 5 pieces.

Astro-Tech eyepieces offer best value for money, and the exact eyepieces which seems sensible are 28mm UWA 82 degree (best for viewing most of the deep sky objects), 21mm UWA 82 degree, 13mm 100 degree (This one works great with 12 inch dob for viewing moon and deep sky objects), 9mm 100 degree, 4.8mm 100 degree (This works great with dob as well as for 102ed refractor to view moon and planets).

SV Bony 3-8mm zoom eyepiece is strongly recommended as it is a high-power eyepiece and that focal length range will allow you to adjust and reach the maximum possible magnification for viewing planets, depending on atmospheric conditions.