When you send an email with your signature, it looks fine because your email client is in reading mode. But when someone replies to your email, their email client is in composing mode. This means that they can edit or modify your signature however they want or need. Some email clients may change the font, size, color, alignment, or layout of your signature. Some may even remove some elements or images from your signature. This is why your signature looks different or messed up on reply emails.
However, this does not mean that the recipient received your signature in a messed up way. In most cases, your signature will look as you intended it to look when the recipient reads your email in reading mode. You can test this by sending yourself an email with your signature and switching to reading mode to see how it appears.
Unfortunately, there is no solution or workaround for this problem when using HTML email signatures. It is just the way that email clients work. The only way to ensure that your signature looks exactly the same on reply emails is to use plain text signatures, but then you will lose all the formatting and images that make your signature stand out.