Can I get my car back if I have disabled children?

Yes

Provided that the disabled blue badge is displayed inside the car when the bailiff took control of it.^[1]

If the disabled badge is not displayed inside the vehicle when the bailiff took control of it, then it is not exempt goods, and the bailiff may take it, provided it is not otherwise exempt for being used in a person's trade, education or business.^[2][3]

^{[1] Regulation 4(1)(d) of the Taking Control of Goods Regulations 2013
[2] Regulation 4(1)(1) of the Taking Control of Goods Regulations 2013
[3] See Making a claim to exempt goods}