If my child opens the door to bailiffs then leaves it open to come to get me can bailiffs enter the house?

Yes

The bailiff may enter the property through any door, or any usual means by which entry is gained.^[1]

Bailiffs must withdraw from domestic premises if the only person present is, or appears to be, under the age of 16 or is deemed to be vulnerable by the enforcement agent; they can ask when the debtor will be home - if appropriate.^[2]

Bailiffs must withdraw without making enquiries if the only persons present are children who appear to be under the age of 12.^[3]

The use of a landlord's key to gain entry is unlawful.^[4]

If the key is found but is not in the lock, the entry would be unlawful.^[5]

If a key is in the lock, the bailiff may gain entry using the key.^[6]

^{[1] Regulation 20(a) of the Taking Control of Goods Regulations 2013
[2] Paragraph 72 of the Taking Control of Goods, National Standards, 6 April 2014
[3] Paragraph 73 of the Taking Control of Goods, National Standards, 6 April 2014
[4] Miller v Curry [1893]
[5] Welch v Krakovsky [1919]
[6] Ryan v Shilcock [1851] 7 Exch 72}