You should be cautious about any dealings with a vanity publisher, they make all their profit by selling you overpriced services. In this case, you're essentially paying for the illustrations (perhaps not as a separate line item, but included in your contract), with no guarantee of quality, and no ownership of the finished images. It's even possible they may not create custom images for you, but draw from a library of stock images (which might be one reason they want to retain copyright).
You might want to look into submitting to a standard publisher. They usually prefer to find the illustrator themselves, so it is perfectly fine (and probably even better) to submit without illustrations included. You still end up not owning the illustrations, but at their cost, not yours. Also, they are likely to be able to afford/access much higher quality illustrations, as well as work with illustrators proven to have a good grasp of the market. Since they make their money off sales, not you, it is in their own interest to get the best possible illustrations, in a way that is not also true for the vanity press.
If you do want to self-publish, I would strongly advise commissioning your own illustrator. That way you get editorial oversight AND copyright. In general, if you're willing to do the legwork and research to find competent work, you can take care of all the services a vanity press does --not always at a lower cost, but with higher quality and more long-term control over the results.