One Server, two IPs, DNS setup

[tbnarvaez at yahoo.com]

I`d appreciate very much any help with the following problem:

I have one web server connect to the internet via Provider A. By the
way, the ip address asigned to that server (IP A) belongs to Provider A
as well as the DNS server I use.
The problem is that link is very unstable and it is constantly out of
service.

Because of this situation I am adding a second internet link with
Provider B who will also assign its own IP address to my web server (IP
B).

In order for this to work I am thinking about doing the following:
a). I will assign to the web server both IP addresses in the same NIC.

b) In Providers A's DNS server I will assign to the web server two IP
addresses: the one assigned by Provider A and the second one from
Provider B.

My questions are:
1. Is this all I should do?
2. Will it be any off time because of the DNS broadcast of the new IP
address (or even the old IP Address)?
3. If link A fails will it be possible for a client to access the web
server via Provider B's link even if the DNS server belongs to Provider
A? 

Thanks in advance for any comments or suggestions.