Answer:
1. Allan spoke with grudging acceptance of  Lalla's engagement to Godfrey. <em><u>vacillating</u></em>.
2. Jane knew she would feel very lonely after  Lalla got married. <em><u>bereft
</u></em>
3. Mother was exasperated with Lalla for  changing her mind so often about the  wedding plans. <em><u>resignation
</u></em>
4. For Lalla's sake, Godfrey and Allan put aside  their intense dislike for each other." <em><u>enmity
</u></em>
5. On the wedding day the weather turned sunny  and mild. <em><u>Benign
</u></em>
6. Before the ceremony, Uncle Peter spoke  distressingly to Godfrey about the  responsibilities of married life. <em><u>unnervingly  </u></em>
7. Remembering Uncle Peter's advice, Godfrey felt  some anxiety about getting married. <u><em>trepidation
</em></u>
8. Aunt Fran arrived wearing a very silly green  feathered hat. <em><u>ludicrous
</u></em>
9. Allan missed the wedding because he could  not figure out the map Barney sent him. <em><u>decipher
</u></em>
10. The ceremony went exactly as planned, and  the organist played the wedding music without  a single mistake. <em><u>impeccably</u></em>
Explanation:
1. Allan spoke with grudging acceptance of  Lalla's engagement to Godfrey. vacillating- it means to hesitate, to be unable to come to terms with.
2. Jane knew she would feel very lonely after  Lalla got married. bereft means to be left alone, to be all alone.
3. Mother was exasperated with Lalla for  changing her mind so often about the  wedding plans. resignation- it means to give up, to be done with.
4. For Lalla's sake, Godfrey and Allan put aside  their intense dislike for each other." enmity- means to have animosity, hatred or dislike for something.
5. On the wedding day the weather turned sunny  and mild. Benign- means gentle, friendly.
6. Before the ceremony, Uncle Peter spoke  distressingly to Godfrey about the  responsibilities of married life. unnervingly- means making someone feel uncomfortable, or giving the feeling of unwelcome, or a worried feeling.  
7. Remembering Uncle Peter's advice, Godfrey felt  some anxiety about getting married. trepidation- means to feel anxious or nervous about something.
8. Aunt Fran arrived wearing a very silly green  feathered hat. ludicrous- this word suggests something that is outrageous, unreasonable.
9. Allan missed the wedding because he could  not figure out the map Barney sent him. decipher- means to understand, to get the main point, to solve, etc.
10. The ceremony went exactly as planned, and  the organist played the wedding music without  a single mistake. impeccably- It means perfect, with no faults or mistakes.