OP, you said you want it to last several years without needing I assume costly or major attention issues/repairs. That's certainly possible with a small sized trailer of 18' but that small sized 18' trailer will always be the same size in one year or in five years however your kids won't. Nor will the toys, their clothes etc, or the amount of food needed to be taken as you'll be in a larger refrigerator needed normally, larger freshwater and holding tanks needed, more floor space needed, etc and it never gets smaller or lesser needed as long as the 4 of you alone are using the TT.
What if your kids, as usually happens, wants to have a friend go camping with them too? The issues just keep on adding as the family gets older and more active inside the trailer as there will always be days it rains all day, gets windy or blowing the rain as you'll need the awning up, or it turns cold or both and you'll all be inside for shelter and heat.
$13K for an adequate new TT for a growing family of 4 that will be reasonable quality to last many years with likely no costly repairs needed mat not be possible. Then the normal things like new tires needed which will happen as the tires on new RV's are almost all the cheapest barely adequate when new is what you'll almost always find. That's about a $500 cost in todays prices alone. Just an example.
You have that capability of towing 8,000 lbs per your post words. Subtract the 4 family members weight and anything like bikes or other thing that will sneak into the mix, around 500 to 1000 lbs for personal items, food-canned or bottled items at 8 lbs/gal, tools, water in tank & water heater (8lbs/gal, propane and batteries which are not light and not included in the TT's dry weight, any other cargo taken. You no longer have 8,000 lbs for the TT itself. Likely down to around 6,000 or less max.
This still allows you to safely pull many 22' to 26' TT models for many years but not likely to find any new ones for $13K. A slide out will sure be a blessing and very important for resale value too. Your future years of camping will sure teach you!
Maybe some additional considering and thinking including the coming future needs to be done. Yes, there will be some movement required on the $13k max or TT size or used VS new, etc, or some combo's thereof. Etched in stone may likely be a very bad thinking with unpleasant results. Smart to juggle some of the fore though parameters set to actually get the best bang for the buck in fun and experiences in life's reality you'll live. Today will be gone tomorrow as will next year on Jan 1 the following year but you and your family will still be aging and can never go back.
We sure have learned a lot about RV'ing, quality, size needed, and being cost effective in our 52 years of RV'ing not only for today but for the future years needs from today as it all changes and you will see and experience this lesson too. Tomorrow comes real quick and finding your having been lost behind in past years can really ruin your present day experiences.
A superb CC LB 4X4, GM HD Diesel, airbags, Rancho's, lots more
Lance Legend TC 11' 4", loaded including 3400 PP generator and my deluxe 2' X 7' rear porch
29 ft Carriage Carri-lite 5'er - a specially built gem
A like new '07 Sunline Solaris 26' TT