All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
We ask Allaah to reward you generously for being so keen on giving your children a good Islamic upbringing, and we implore Him to help you accomplish that objective and instill into their hearts and minds correct faith and noble manners and virtues of Islam. We advise you to supplicate Allaah, The Exalted, for your children; verily, parents’ supplication for their children is accepted.
Sending Muslim children to a kindergarten run by non-Muslims is a serious issue and its evil consequences are obvious; therefore, you should beware of that in any case. If your husband prevents you from taking his daughter to the Masjid, then you are obliged to obey him.
If you go to the Masjid only for the purpose of performing the prayer, then you should know that performing the prayer at home is better for a woman and more rewardable than performing it in the Masjid. Ibn ‘Umar reported that the Prophet said: “Do not prevent your women from going to the Masjid; and their houses are better for them (for praying).” [Ahmad and Abu Daawood]
However, if you go to the Masjid for the purpose of seeking knowledge and carrying out righteous deeds therein, then this is commendable and in this case you are obliged to adhere to Hijab and modesty. If you can find someone reliable and trustworthy to take care of your daughter while you are in the Masjid, then that would be fine; otherwise, you should find another means for seeking knowledge. Verily, there are many means for acquiring knowledge available now such as through the internet and the like.
There is no harm in cooking special meals for your children on Jumu'ah (Friday). It is a commendable custom and a manifestation of generosity towards the children on that day, and, normally, it is not intended to be an act of worship. Therefore, calling it a Bid'ah (religious innovation) is incorrect.
Allaah Knows best.