That is incorrect understanding of the halakha. In short, there is a very clear history of women who wore Tallit and Tephilin, the daughters of Rashi are the best known examples. Again, this is a very simplistic explanation of the issue, but just wanted to point out that it is definitly not viewed by halakha as akin to tranvestitism. Doing this runs counter to the notion of one way of Jewish practice and belief handed down from Sinai. I will go farther than Alex.
Parents also deserve the opportunity to raise their children.
In general this would be a good thing. However, too many exceptions make it bad policy to exclude other kinds of family units from mainstream Judaism. So we will always have single parents and remarried parents. You may make your own choices. I am a living counterexample, and I find your advice repugnant.