The permissibility of carrying children during prayer, and their garments are regarded as being pure until it is realized that they are impure. Few actions will not invalidate the prayer, and the same applies if several such actions are done but are done separately
حَدَّثَنَا مُحَمَّدُ بْنُ أَبِي عُمَرَ، حَدَّثَنَا سُفْيَانُ، عَنْ عُثْمَانَ بْنِ أَبِي سُلَيْمَانَ، وَابْنِ، عَجْلاَنَ سَمِعَا عَامِرَ بْنَ عَبْدِ اللَّهِ بْنِ الزُّبَيْرِ، يُحَدِّثُ عَنْ عَمْرِو بْنِ سُلَيْمٍ الزُّرَقِيِّ، عَنْ أَبِي قَتَادَةَ الأَنْصَارِيِّ، قَالَ رَأَيْتُ النَّبِيَّ صلى الله عليه وسلم يَؤُمُّ النَّاسَ وَأُمَامَةُ بِنْتُ أَبِي الْعَاصِ وَهْىَ ابْنَةُ زَيْنَبَ بِنْتِ النَّبِيِّ صلى الله عليه وسلم عَلَى عَاتِقِهِ فَإِذَا رَكَعَ وَضَعَهَا وَإِذَا رَفَعَ مِنَ السُّجُودِ أَعَادَهَا .
Abu Qatada al-Ansari reported: I saw the Apostle (ﷺ) leading the people in prayer with Umima, daughter of Abu'l-'As and Zainab, daughter of the Messenger of Allah (ﷺ), on his shoulder. When he bowed, he put her down, and when he got up after prostration, he lifted her again.