I have a 2004 Venture Van, 3.8l with 145,000 miles. I have been towing a 2 axle car trailer with a cavalier race car on it, estimated total weight of 3500lbs. I have installed air shocks on the rear and am told the hitch is rated for 5000 lbs. Am going to a larger race car (Monte carlo) (estimated weight 4000 lbs) and am wondering if I will still be able to pull the car and trailer with the Venture. The transmission has been serviced with fluid changes previously but has no transmission cooler.
The Venture isn’t a van. It’s a minivan, and I think you’re already pushing the limit of towing with it. I wouldn’t try to tow more.
Do you have a friend with a full size truck? Tow the car and trailer to the nearest truck stop and weigh them so you know exactly how much they weigh. Then take a close look at your owner’s manual. I’m willing to bet the Venture’s towing capacity is 3,500# or less.
Yep, specs are 3500, so you’re over that with the new car (and maybe the current one). I’d want at least 5,000 pounds towing capacity for what you describe.
The Venture never had the 3.8L. The 3.4L was the only engine offered. I’d say you’re currently at the limit the vehicle is rated for with the factory towing package (which would’ve included a transmission cooler), without the cooler, even now you’re rolling the dice towing that kind of weight with the vehicle as is. With the new racecar you’ll be over the weight limit.
A half ton truck or full sized van is a much better choice than what you’re currently using.
Your load is severely overtaxing the van’s capacity. If you don’t have electric brakes you are also dangerously overtaxing the van’s brakes. Very dangerous!
A mini-“van” is really a maxi-“wagon.” In other words, it’s not a small van, but a tall station wagon. The drive trains in them are frequently the same drive trains a manufacturer puts in their full size sedans (or wagons when they still made wagons). Nothing about them is actually made the way full sized van’s are. They are also unibody frames, for example. I wouldn’t tow a thing with a mini"van" and since you’re already at capacity - as all of the others have said - no, you can’t tow this one with it.
I wouldn’t even put it that way. Minivans have almost all been closely related to mid-sized car platforms and some small trucks. The original Chrysler minivans were close relatives of the K-Car. The Ford Aerostar and Chevy Astro were most closely to the Ranger and S10 trucks. The Toyota Van/Previa was unique here, but a common commercial van there. I think the Mazda MPV had some 626 ancestry.
Of current vans, they’re often designed jointly with crossovers/SUVs. The Sienna, like so many Toyota’s, is based on the Camry, as are the Avalon Venza (basically a Camry wagon), Lexus EX, Highlander, Pathfinder, Lexus RX, and probably another I haven’t thought of. Not a dud in the bunch.
The Honda Odyssey is loosely related to the Accord, and closely related to the Crosstour, Pilot, Ridgeline, Acura TSX, TL, and MDX. Maybe even the Acura FX and that goofy fastback crossover they discontinued.
The Kia Sedona is based on cars that are long since dead. The current Chrysler models are based on the 200 and maybe some DNA from the Durango.
The Ford Flex is an outgrowth of the Taurus X, which was renamed FreeStyle, based on the Five Hundred, a name Ford used for a very few years instead of the better known Taurus. Anyhow, a Flex is essentially a Taurus wagon in the same way a Venza is a Camry wagon.
I know we have discussed this many times before, but @cigroller and others make sense to me. We really don’t know how reinforced the unibody is and how capable it might be. But, we do know as cig and others say, it is at it’s tow rating limit. I would add, it’s ten years old too and unlike the rest of us, cars don’t improve with age. As far as being derived from sedans, yes they are. But, a Highlander with a Camry six and heritage and a tow package which includes a cooler and special hitch, is rated to tow 3500 lbs. That’s as much if not more then my Toyota pick up with a full ladder frame. I know that many ratings may be a little suspect but at least according to the manufacturer, it’s more about how something is made then what “gave birth” to it. 
I also agree with @texases that you should be significantly under your rated capacity for safe towing and 5000 lb capacity seems quite reasonable. That means if money is an issue, you may be looking at half ton pick ups but you may not have to avoid unibody vehicles, just some of them. Jeep for one is quite high.