With a 9 year old in tow go early season do an antelope hunt public land in Wyoming then swing down to Northern Colorado for an over the counter bull or draw cow tag. If you have a camper or trailer already you'll have at least a grand left over. You can apply for a tag in Wyoming fairly soon and Cow tag in Co before April or leftover in August.
Staying in hotels cabins etc probably can be done under that budget even with a cow,bull and antelope tag.
That assumes you have a truck or good hunting vehicle, rifle rangefinder, boots etc. Upgrading your elk hunting gear can be habit forming and expensive.
My dad and I never made the elk hunt we talked about and that might be the biggest regret that I have. Take your son this year and get that Rocky Mountain elk hunting bug. I'm dragging my grandson out this year he turns 12 and will be carrying a rifle. I expect he will talk about it the rest of his life.
