Although a person should be allowed to make an act of contrition and given a penance, the absence of those elements does not invalidate a confession. However, if absolution is not given, then absolution has not been given. In other words, if the priest did not absolve your daughter of her sins, then your daughter did not receive absolution.
If we want to put the most positive spin on the priest’s actions, it may be that he did not think that your daughter had sinned and so did not think absolution appropriate. But if she confessed venial sin and there was no reason to deny her absolution, your priest should have absolved her (and, by your daughter’s account, the priest’s exhortation that she “try to do better” does suggest that she confessed venial sin). The Church strongly encourages the confession of venial sins (CCC 1458) and consistent confession in childhood is the best preparation for a lifelong commitment to the sacrament of reconciliation.
There are two problems here: The immediate problem of what to do for your daughter and the larger problem of this priest’s reported approach to children’s confessions.
Solving your daughter’s situation is relatively easy. Explain to her that Father “may have made a mistake” by not granting her absolution – the qualification will show respect for the priest, something important to model for and encourage in children – and that you will take her to another priest to repeat her confession. Before her confession, it might be wise to explain the situation to the second priest so that your daughter will not have to.
As to the larger problem: Since your daughter is only seven and seven-year-olds can make mistakes in their reports of events, it is possible that your daughter’s report of the confession may not be entirely accurate. I recommend making an appointment with her original confessor. Explain that you understand that he cannot discuss your daughter’s confession with you, but that you want to let him know of your daughter’s report of the confession to you. Then tell him what she said. That will likely be the extent of the conversation, given that the priest cannot discuss your daughter’s confession, but at least he will be made aware that children are leaving his confessional confused as to whether they have been granted absolution.