A convalidation is when someone has been married civilly but due to an impediment the marriage was invalid as a sacrament. The impediment must first be removed and the couple then makes a new exchange of vows to enter into a sacramental marriage.
The usual impediment would be what's called lack of canonical form, which is marrying outside the Church without permission. In such a situation a new exchange of vows is performed in the Catholic form in order to make it valid.
In the situation you describe, the impediments to be removed are twofold:
1. prior marriage bond (your husband's first marriage).
2, lack of canonical form (being married outside the Church, presuming you were Catholic at the time).
The annulment is what addresses the prior marriage bond. Until that prior marriage bond is declared null then nothing else can move forward.
The good news is that if the prior marriage is determined to be null, then the convalidation can take place fairly quickly.
The unfortunate news is that unless that determination is made prior to your child's first communion then there is nothing the local parish can do to address your situation.
Please don't feel discouraged, you are doing the right steps to address your situation and God willing it will be reach a solution soon.