I don't know of any resins that do not off-gas some form of noxious, possibly toxic, odors, but most of them don't gas enough to be harmful in a large room with adequate ventilation. Most of them don't even smell bad except when working close to the mix.
Adequate ventilation, basically, means if you can smell it from more than a couple feet away, another window should be opened or another fan turned on to suck it out of the room.
Bottom line is what you smell during a mix/pour is either petrochemical or synthetic chemical off-gassing, and that stuff can be harmful, but not necessarily so. If you can smell it, why take a chance? A good, reusable 3M respirator with NIOSH filters for fumes runs around $20 in most hardware stores. I figure if I can afford $20 for 16 ounces of mix I can sure afford to protect my much more expensive lungs and other organs.
My opinion would be to not expose small children to the fumes at any time. Keep the room in which the pour is done and project cured (resins off-gas until done curing) off limits to children and door(s) closed so they cannot enter.
Check labels to see if the State of California has put any of the ingredients on their cancer list. Check each product's MSDS (Material Safety Data Sheet) and comply with all safety precautions. Manufacturers are required by Federal law to provide an MSDS for every chemical they make/sell. If they balk at letting you read it, don't use the product.
.....I'm guessing your wanting to make a tumbler as in a drinking glass........
First off it's really doubtful that you would be using enough mold making material/resin to generate a health hazard, either to you, your daughter or neighbors. Proper ventilation is always good practice, teaching children of a learning age something like a hobby or craft is even a better practice verses scaring them off with a perceived risk scare.
I have never used a respirator with ANY of Alumilites products that I have ever used....I have just finished going thru the Alumilte printed info.,yet again, that has been made available to me and no where does it even hint to the idea that any of their products, that the average hobbyist would use, is indeed a health hazard that poses a risk to your lungs or other body organs or bodily functions.
Here is a direct quote from one of their publications: "Alumilites casting resins are non-toxic and virtually oderless. First of all, we recommend you read any and all MSDS (Material Safety Data Sheets) and warning label on any product that you use. All urethanes contain some type of Isocyanate. We have a very small, diluted amount of MDI Isocyanate, which was deregulated as hazardous and is not considered to be a hazardous material. Alumilite contains no mercury, (found in many other urethanes). Alumilite is not considered to be carcinogenic. Alumilite is safe for home use.
California's cancer list is a complete joke....have you actually taken time to read it? If anyone bothers to fallow it , they would soon find out that there is very few consumer items that could be consumed/used/purchased at the risk of causing cancer in California. Alumilite makes MSDS information available to anyone....either at point of purchase or upon request.
Both ohmo and Brian have good points - provide good ventilation and you will be fine. Now as for letting children learn crafting, I've always felt that learning young with good supervision is key to helping a good child become a smart and constructive child. I learned crafting stuff in my early teens and I've always been very good with my hands and making things. So I fully support teaching children how to do things - it will be just fine as long as you are supervising them.
For the off gassing, any fumes, and/or smell - I have allergies (and am sensitive to fumes), a mostly open area, two dogs in the house, and when I measure or mix Alumilite products I bring my eyes (and nose) to within inches of this stuff and I can't smell a thing 9 1/2 times out of ten. I have never used a respirator while working and half the time I forget to use a fan just to move the air since it's gotten cold outside. Of course the room I use is open on two ends so it's fairly well ventilated as is. If you are very worried about the fumes, bring an air purifier (with a HEPA filter) into the room and keep it as close to your work area as possible.
In other words, you should be just fine as long as you take proper care. If you open a can of paint and get overcome by the smell right away then you might not have good ventilation as paint would be a lot stronger smell than any of the resins.