The agreement is written very broadly to include any business competing "directly or indirectly."
Whether the Majority Member's prospective business is actually competing is a question of fact which would be answered by a jury. If, for example, the member invests in another restaurant which is in the same area of town, or the exact same kind of cuisine in the same city, then there would be a strong argument that this is a competing business.
The consequence of a breach of the agreement would be that you could seek damages. Damages can come in the form of an actual loss in revenue caused by the breach, loss of future profits, loss of the value of the business, or loss of the investment
made to get into the business.
If your wife does not sell, it is definitely possible that a merger could occur which would dilute your wife's interests. A merger, or grant of new memberships, reduces everyone's share proportionately. It can be approved by the Majority shareholder
alone. So he can force it on your wife.
The thought that they want all the profits to themselves is probably true. However, its reasonable for them to want to buy her out if she is not going to be a working partner.
So, in reality, you are looking at being forced into the merger, with a reduction of your share of the profits corresponding to that, OR can agree with a buy out and try to negotiate a higher purchase price.
The other reality is that the Majority member can simply shut the business down.
However, the majority member cannot open a competing business, so the merger is more likely to occur than the majority member breaching. If the majority member breaches, you can sue him.