All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Fulfilling one’s promise is desirable and not an obligation according to the view of the majority of the scholars ; however, fulfilling it is very much desirable and it is vey much disliked to break it. Allaah Says (what means): {And fulfill [every] commitment. Indeed, the commitment is ever [that about which one will be] questioned.}[Quran 17:34]
Therefore, in principle, it is desirable that you fulfill your promise to her and not marry a second wife, but if the situation is as you mentioned that you desire to marry another wife and you are not satisfied with one wife, then marriage could be an obligation in your regard if you fear to commit illegal sexual intercourse. Hence, it is permissible for you to marry a second wife if you are able to be just between them with regard to spending the night with them, providing for them, etc. For more benefit, please refer to Fatwa 95416.
On the other hand, you are not obliged to please your present wife, but if you can convince her, then it is better. It is natural that a wife is not pleased that her husband marries a second wife, but you should not refrain from marrying (a second wife) just because of this, since marriage leads to many advantages. Therefore, a Muslim woman should consider this and not be egoistic wanting to only achieve her interests and not consider the interests of others; for more benefit, please refer to Fatwa 90132. For more benefit on the objectives of the Sharee’ah in polygyny, please refer to Fatwa 86818.
As regards her being or not being your only wife in Paradise, then the matter is not in your hands; this is a matter that is purely in the Hands of Allaah, so how can she ask you to make an oath on this. In addition to this, in Paradise there is no jealousy or harm between the wives like it is the case in this worldly life.
Nonetheless, we advise you not to talk too much about the matter of marriage with her as this hurts the wife in general. If it happens that she raises the issue, then you should try to comfort her with some good words, like saying to her that marrying a second wife would not decrease your love to her, and other good words.
After all this, we say that if you fear that your family will be broken up if you marry a second wife, or fear other harms, then it might be better for you to be satisfied with your present wife, and to try to keep yourself chaste by fasting and other things that may diminish your sexual desire.
Allaah Knows best.