May a Jewish Orthodox wife stop wearing her wedding ring after marriage? Can she specify that she will not wear it untill she has children?
For a good review of the significance of the wedding ring in Judaism, I recommend the section entitled "The Marriage Ring" of the book The Jewish Way in Love & Marriage, by R' Maurice Lamm. As R' Lamm explains, the technical purpose of the wedding ring is to serve as part of the binding transaction that establishes the marriage.
While there's plenty of literature on the significance of using a ring, in particular, for this purpose, there's no requirement in Jewish Law for the wife to actually wear the ring;1 all she needs to do is to accept it for the purpose of marriage at the wedding itself.
1. At least, there isn't one mentioned in this piece by R' Lamm, and there isn't one that I've ever heard of in my 3+ decades as an observant Jew.
Halachically speaking a person does not have to use a ring for kiddushin (thus the woman need not wear it). Additionally, after the ceremony is over, the wife does not have to keep whatever object that she was given (unlike the kesuvah).
However, it has become a standard custom in our society for the wife to wear a wedding ring as a sign that she is married. On the other hand, there are times when a woman (or man) would not wear a ring for practical reasons. As an example, consider someone who deals with delicate machinery or some other situation in which wearing metal could be dangerous.
What does need to be considered would be if people think that she is not married and treat her as an unmarried woman. Also if she is seen with her husband (acting as a wife), it could be a matter of mar'is ayin. If she does stop wearing the ring, people may think that the marriage is in trouble or, chas veshalom, even that they have been divorced.
According to most poskim, it is permitted to effect Kiddushin with a borrowed ring if the person you are borrowing it from knows that you’re using it for Kiddushin.17 However, to avoid a dispute one should borrow the ring from the third party as a matana al menat lhachzir (a gift given on condition that it is later returned).18
If the ring gets lost, it is possible to do the Kiddushin with a coin.19
the only possible problem that comes to mind in stopping to wear it is that she already started to do it and might have done it with the plans to continue to do it (similar to the case of washing the whole hand see halacha 8 here
It is, however, correct to stipulate that one is not accepting this practice as an obligation, but rather as a voluntary act. Thus if on a given occasion, he does not have sufficient water, he need not observe this stringency as is his ordinary practice. Indeed, it is proper to make a similar stipulation regarding all stridencies that a person desires to accept upon himself.
...Israel is accustomed to preform the betrothal with a ring, so that it be a constant commemoration on her hand)
so to stop wearing it she might needs to nullify the possible vow by a Rav
it seems that by specifying that she will not wear it until she has children
she might be making another vow/oath which is not advisable.
PS obviously if her husband wants her to wear it, it is good for her to continue to wear it, even if by law she is not obligated to do so (see other answers), see halacha 20 here and end of halacha EH 69:7 here
PPS if it is bothering her for example when she is kneading the dough obviously she can take it off
see halacha 7 here
if the person is particular about removing the ring at times, e.g., the ring has a precious stone and he is careful about removing the ring before washing so that the water does not soil it. Women are careful to remove even a ring that does not have a precious stone when kneading dough.
As for the accepted presentation of a ring at the time of Kedushin, originally any item with a value of at least one PRUTA was the norm. A ring probably became the prefered item was because it can be worn, while performing many other household tasks. However in today's world, probably a more practical item would be a wrist watch. Why? so that the wife knows how to schedule her day in order to get the meals on the table at the proper time. But there is no real obligation to actually wear the gift used at the time of Kidushin.