Answer: The Gemara (Shabbos 125b) writes that it is forbidden to build a temporary ohel, tent, on Shabbos. Rambam (Shabbos 22:27) explains that building a permanent ohel is a tolda of boneh, building, and therefore assur mideoraisa. Chazal made a gezeira, decree, that one shouldn’t build a temporary ohel to prevent one from making a permanent one. Thus, the Mishna Berura (315:1) writes that one mustn’t spread out mats or sheets like a tent on Shabbos.
The Shulchan Aruch (OC 315:2) writes that if the ohel existed already, then one may add to it. Thus, one may place long tablecloths over tables or add to other structures, providing the roof is at least a tefach wide.
Nonetheless, the Shulchan Aruch (OC 315:3) and Mishna Berura (315:17) write that one may build a temporary structure if they construct it in a backwards manner. Thus, one may hold up the roof and build the walls under it.
Likewise, the Shulchan Aruch (OC 315:4) writes that one mustn’t dismantle an ohel on Shabbos. Yet, R’ Yehoshua Neuwirth (Shemiras Shabbos Kehilchasa 24:22) writes that one may do so in a backwards manner, that is by raising the roof and dismantling the walls before lowering the roof.
In conclusion, as creating tents out of blankets on Shabbos is problematic, one needs to teach one’s children to build them in a backwards manner, or create them before Shabbos.