"Firing" a bridesmaid is a pretty serious thing and signifies that you are ending the friendship with her. Feelings are hurt enough to make severing the friendship permanent. If she is family (including a FSIL), that adds another twist... It can cause hard feelings and resentment among family members, and possibly even a rift among your relatives as people begin to take "sides".
To summarize, here are some of the difficulties that people run into and the most often recommended solutions:
1. Overenthusiastic bridesmaid. Bridesmaid is too involved with the planning and tries to foist her opinions/ideas on the bride. Some can get pretty controlling into the bargain.
Step back and take a deep breath. Realize that she's probably just overenthusiastic. Don't discuss your wedding plans with her. Don't talk to her for a while. If she's unavoidable and still giving suggestions, simply say "Thanks for your input, but we've already decided what we're going to do for that," and don't go into detail. Say that often enough, she'll eventually realize that you're not interested in her ideas.
2. Jealous bridesmaid... usually jealous of the fact that your getting married and she's not. This can manifest itself in so many ways: Lack of enthusiasm with wedding-related activities (showers, bachelorette party), derogatory comments about marriage in general, or more personal attacks on how she doesn't think you and your FI are right for each other.
First, if she's saying hurtful things, a good heart to heart talk may help. Tell her that her negative comment (be specific) really hurt your feelings. Most of these people don't realize how hurtful they are until it's been called to their attention.
Beyond that, give her lots of space. Don't talk to her about anything wedding related except for ordering dresses and getting measured for them. A few weeks before the wedding, give her the rehearsal time and necessary details, but don't talk about any other details. Don't require/expect any more from her than buying a dress and standing next to you during the wedding.
3. Reluctant bridesmaid. Hard to get in touch with (returning phone calls, e-mails). Lack of enthusiasm about anything wedding related (showers, bachelorette party). Evavise about the necessities of her part in the wedding (e.g. ordering a dress, getting measured, etc.). Complains about the style of dress, other items she's required to purchase (shoes, hair & makeup) or financial obligations of buying it.
First, remind yourself that your bridesmaids only have two obligations: buying a dress and standing next to you during your wedding. Anything else they do beyond that (e.g. throwing a shower... or even attending the shower) is out of the goodness of their hearts and not a requirement. If they can't make the rehearsal because of a conflict, don't worry about it. Conflicts happen sometimes. If you have other bridesmaids, they'll be able to fill in this one on any instructions if she missed the rehearsal.
Some bridesmaids experience real financial pressures, and this can make them reluctant. If you're able to, help her with the cost of her dress. Help all your BM's save a little money by having them wear neutral color shoes (e.g. black, beige) they already own. Allow them to do their own hair and makeup.
Regarding the style of the dress, if she's a different size/shape, allow her to wear the same color dress but a different style, if she's not comfortable with the style the others are wearing.
The other side of the coin is a bridesmaid who is impossible to get in touch with about the necessities of the wedding, such as buying her dress. Remember she can go to the shop on her own schedule, you don't have to go together. Just give her a deadline - "You need to be measured and order your dress at the shop no later than X date." After that leave the ball in her court. If she waits too long and doesn't order a dress, then kindly tell her you understand (whatever excuse it is), and she's welcome to attend your wedding as a guest.
4. Friendship gone sour. It happens. Friendships can change over time and suddenly turns a Ms. Jekyll into a Ms. Hyde.
The most important thing to ask yourself here is if you are ready to end the friendship and sever ties with this person. If you feel like the friendship is one you want to keep, take her to lunch and ask her what's on her mind. Don't mention anything about the wedding - keep the focus on her and what may be going on in her life. You may discover she's been having a difficult time with a situation that recently came up (example - her boyfriend dumped her, a family member just got diagnosed with cancer) and she didn't want to bother you with is since she knew you were deep into wedding planning. Tell her that your friendship is important to you and you'd like to help if you can.
If you've tried being diplomatic, including the above suggestions, and she really can't be reasoned with, only then should you consider telling her that you feel it would be easier on BOTH of you if she attended your wedding as a guest instead of part of the bridal party. This does cause hard feelings, no matter how you word it though. The ultimate outcome is that it will end the friendship.