Hi, I would think your looking more towards a van derived vehicle to stow a wheelchair unfolded. Depending on the dimensions of your daughters pushchair, its possible it would go in on its side in a large car or estate.
However you may struggle to find anything with an advance payment of £500 max. You could try and apply for a grant to help towards the advance but I honestly don’t think they will take into account the fath of unfolding it sorry.