It ispossible. Legal? That I dont know.. I sort of agree with you on the idea that it is THAT PERSONS child.... so in a morbid sense , they can do as they wish

But then again... well.. I dunno.
You remember that singer Marilyn Manson?
He has a child preserved in his home . It has been proven, photographed... ( he is wierd to say the least..) but HE has done it. he also has millions of dollars to allow him to do that if there were any legal reprocussions to it, he could afford to get out of it.
Formaldehyde is usually used to preserve organic material (tissues, organs etc..) and according to size/weight of specimine, it is entirely POSSIBLE to preserve a baby in ones home because it would only take a small amount. Meaning... you wouldnt have to have an enormous container to keep the specimine in.
I believe.... if I remember correctly, 1/2 cup per 1 lb of tissue is what is needed. If a child were about 7 lbs, then they would only need a container about the size of a small book box to properly preserve the tissue.
However... I PERSONALY would question the stance taken on wanting to keep a baby preserved in that way in ones home. But that is just my opinion.
But, to answer your question.. yes.. it is possible.
I dont know that you would find anything about it being legal? if I were to break it down, I would think that it is entirely legal. The natural child of a parent , in the legal sense, BELONGS to them. Even in death. We have the right to choose HOW we want our children burried.. so I would think we would have the right to choose to preserve them? You think?
I could be wrong.. but I dont know that there are such laws in place to prohibit someone from doing that.
Mummified remains would be a very hard thing to accomplish for the average person. Not only would it take alot of time, but you would have to be able to afford and arrange the perfect atmosphere to allow the mummification to take place. Scientists do it alot. I remember when we were studying the break down of human tissues after death in school, I got to see an artifically created mummy. MAN! that was WAY cool... but it took 2 years in a lab to get the desired outcome. I couldnt imagine the regular family being able to afford that , or for that matter, having access to people who WOULD do that for them.
If this family has a 'baby mummy' that they claim is thier child, I would want to see it.... I wouldnt believe them.
( up, you guessed right.. im wierd ;-) )