Welcome!!!
The biggest issue you will hve with the Explorer is the available payload of the vehicle. There is a yellow sticker in the drivers door jamb that states "Passengers and cargo not to exceed XXX(X)lbs". This amount is the max rated payload for YOUR vehicle. The weight of all passengers, any accessories added to the vehicle (step bars, bed liner in trucks, hd floor mats, etc), any coolers or firewood, bikes, the wdh (weight distribution hitch) AND the trailers tw (tongue weigh)t!!!
What are the specs of the trailer? The manufactures "brochure" dry tw does not include the propane tank(s) or battery weight on the tongue. Not sure if that has 1 or 2 propane tanks: 2-20lb tanks and a battery are about 120lbs, so maybe about 85lbs for 1-20lb tank and a battery.
For a safe, stable tow you will want around 12-15% of the loaded trailer weight to be tw. Meaning if you placed a scale under the tongue, a 5klb trailer would have between 600lbs-750lbs of tw. This varies some between trailer models (some like more tw, some tow fine with a little less) and of course, how you pack the trailer. So to help figure out if you have a tv (tow vehicle) that is capable for the trailer you have picked, a lot of rv'ers suggest to use 13% of the trailers gvwr to estimate the loaded tw. Example: GVWR=5klbs, estimated tw= 650lbs toward the Explorer's payload, plus all the passenger and cargo weight to see if the tv will safely tow the trailer.
Post all the #'s of the trailer you are looking at, your aproximate total family weight, the yellow sticker payload of the Explorer, and we will try to do our best to help you.
The thing to remember comcerning the Explorer's payload, your 4 kids are going to continue to grow, making the available payload for the tw even less. While this trailer may be ok now (pending the all the info being posted), in a couple yrs or so the Explorer may be overloaded.