A woman should obtain her husband's permission to perform i’tikaf [spiritual retreat]. On his part, he should not refuse her request without a valid reason. The need to look after a young child, as in this case, is certainly a valid reason. The woman in this case should realize that looking after her baby is a more important duty than performing the Sunnah of i’tikaf.
Having said that, I advise the woman that she can perform as many voluntary devotional acts at home as she wishes, but this does not come under i’tikaf, because that Sunnah must be done in a mosque. Still it entails a great reward but she must not neglect her duties such as attending to her young child.
And God the Almighty knows best.